אריאל

02-10-2009, 12:02

נתון n הוא מספר טבעי.

עבור אילו nים הביטוי n^4+4 הוא מספר ראשוני?

ניחושים לא מתקבלים ( שכן זו לא הוכחה.. )

בהצלחה !

עבור אילו nים הביטוי n^4+4 הוא מספר ראשוני?

ניחושים לא מתקבלים ( שכן זו לא הוכחה.. )

בהצלחה !

צפה בגרסה המלאה : [אלגברה] מספרים ראשוניים

אריאל

02-10-2009, 12:02

נתון n הוא מספר טבעי.

עבור אילו nים הביטוי n^4+4 הוא מספר ראשוני?

ניחושים לא מתקבלים ( שכן זו לא הוכחה.. )

בהצלחה !

עבור אילו nים הביטוי n^4+4 הוא מספר ראשוני?

ניחושים לא מתקבלים ( שכן זו לא הוכחה.. )

בהצלחה !

Hurricane

02-10-2009, 14:20

קודם כל, n חייב להיות אי זוגי.

בדקתי עם מחשב עד n=1000 ומצאתי שזה מתקיים רק כאשר n=1.

עכשיו רק צריך למצוא הוכחה. :P

בדקתי עם מחשב עד n=1000 ומצאתי שזה מתקיים רק כאשר n=1.

עכשיו רק צריך למצוא הוכחה. :P

-רון-

02-10-2009, 14:54

לא מכל מספר ראשוני שמפחיתים ממנו 4 מקבלים מספר ראשוני נוסף! :)

lori

02-10-2009, 14:56

אה באמת? אפשר דוגמה? :)

Hurricane

02-10-2009, 14:58

5 ו- 13.

2 is prime.

3 is prime.

5 is prime.

7 is prime.

11 is prime.

13 is prime.

17 is prime.

19 is prime.

23 is prime.

29 is prime.

31 is prime.

37 is prime.

41 is prime.

43 is prime.

47 is prime.

53 is prime.

59 is prime.

61 is prime.

67 is prime.

71 is prime.

73 is prime.

79 is prime.

83 is prime.

89 is prime.

97 is prime.

101 is prime.

103 is prime.

107 is prime.

109 is prime.

113 is prime.

127 is prime.

131 is prime.

137 is prime.

139 is prime.

149 is prime.

151 is prime.

157 is prime.

163 is prime.

167 is prime.

173 is prime.

179 is prime.

181 is prime.

191 is prime.

193 is prime.

197 is prime.

199 is prime.

211 is prime.

223 is prime.

227 is prime.

229 is prime.

233 is prime.

239 is prime.

241 is prime.

251 is prime.

257 is prime.

263 is prime.

269 is prime.

271 is prime.

277 is prime.

281 is prime.

283 is prime.

293 is prime.

307 is prime.

311 is prime.

313 is prime.

317 is prime.

331 is prime.

337 is prime.

347 is prime.

349 is prime.

353 is prime.

359 is prime.

367 is prime.

373 is prime.

379 is prime.

383 is prime.

389 is prime.

397 is prime.

401 is prime.

409 is prime.

419 is prime.

421 is prime.

431 is prime.

433 is prime.

439 is prime.

443 is prime.

449 is prime.

457 is prime.

461 is prime.

463 is prime.

467 is prime.

479 is prime.

487 is prime.

491 is prime.

499 is prime.

503 is prime.

509 is prime.

521 is prime.

523 is prime.

541 is prime.

547 is prime.

557 is prime.

563 is prime.

569 is prime.

571 is prime.

577 is prime.

587 is prime.

593 is prime.

599 is prime.

601 is prime.

607 is prime.

613 is prime.

617 is prime.

619 is prime.

631 is prime.

641 is prime.

643 is prime.

647 is prime.

653 is prime.

659 is prime.

661 is prime.

673 is prime.

677 is prime.

683 is prime.

691 is prime.

701 is prime.

709 is prime.

719 is prime.

727 is prime.

733 is prime.

739 is prime.

743 is prime.

751 is prime.

757 is prime.

761 is prime.

769 is prime.

773 is prime.

787 is prime.

797 is prime.

809 is prime.

811 is prime.

821 is prime.

823 is prime.

827 is prime.

829 is prime.

839 is prime.

853 is prime.

857 is prime.

859 is prime.

863 is prime.

877 is prime.

881 is prime.

883 is prime.

887 is prime.

907 is prime.

911 is prime.

919 is prime.

929 is prime.

937 is prime.

941 is prime.

947 is prime.

953 is prime.

967 is prime.

971 is prime.

977 is prime.

983 is prime.

991 is prime.

997 is prime.

1009 is prime.

1013 is prime.

1019 is prime.

1021 is prime.

1031 is prime.

1033 is prime.

1039 is prime.

1049 is prime.

1051 is prime.

1061 is prime.

1063 is prime.

1069 is prime.

1087 is prime.

1091 is prime.

1093 is prime.

1097 is prime.

1103 is prime.

1109 is prime.

1117 is prime.

1123 is prime.

1129 is prime.

1151 is prime.

1153 is prime.

1163 is prime.

1171 is prime.

1181 is prime.

1187 is prime.

1193 is prime.

1201 is prime.

1213 is prime.

1217 is prime.

1223 is prime.

1229 is prime.

1231 is prime.

1237 is prime.

1249 is prime.

1259 is prime.

1277 is prime.

1279 is prime.

1283 is prime.

1289 is prime.

1291 is prime.

1297 is prime.

1301 is prime.

1303 is prime.

1307 is prime.

1319 is prime.

1321 is prime.

1327 is prime.

1361 is prime.

1367 is prime.

1373 is prime.

1381 is prime.

1399 is prime.

1409 is prime.

1423 is prime.

1427 is prime.

1429 is prime.

1433 is prime.

1439 is prime.

1447 is prime.

1451 is prime.

1453 is prime.

1459 is prime.

1471 is prime.

1481 is prime.

1483 is prime.

1487 is prime.

1489 is prime.

1493 is prime.

1499 is prime.

1511 is prime.

1523 is prime.

1531 is prime.

1543 is prime.

1549 is prime.

1553 is prime.

1559 is prime.

1567 is prime.

1571 is prime.

1579 is prime.

1583 is prime.

1597 is prime.

1601 is prime.

1607 is prime.

1609 is prime.

1613 is prime.

1619 is prime.

1621 is prime.

1627 is prime.

1637 is prime.

1657 is prime.

1663 is prime.

1667 is prime.

1669 is prime.

1693 is prime.

1697 is prime.

1699 is prime.

1709 is prime.

1721 is prime.

1723 is prime.

1733 is prime.

1741 is prime.

1747 is prime.

1753 is prime.

1759 is prime.

1777 is prime.

1783 is prime.

1787 is prime.

1789 is prime.

1801 is prime.

1811 is prime.

1823 is prime.

1831 is prime.

1847 is prime.

1861 is prime.

1867 is prime.

1871 is prime.

1873 is prime.

1877 is prime.

1879 is prime.

1889 is prime.

1901 is prime.

1907 is prime.

1913 is prime.

1931 is prime.

1933 is prime.

1949 is prime.

1951 is prime.

1973 is prime.

1979 is prime.

1987 is prime.

1993 is prime.

1997 is prime.

1999 is prime.

2003 is prime.

2011 is prime.

2017 is prime.

2027 is prime.

2029 is prime.

2039 is prime.

2053 is prime.

2063 is prime.

2069 is prime.

2081 is prime.

2083 is prime.

2087 is prime.

2089 is prime.

2099 is prime.

2111 is prime.

2113 is prime.

2129 is prime.

2131 is prime.

2137 is prime.

2141 is prime.

2143 is prime.

2153 is prime.

2161 is prime.

2179 is prime.

2203 is prime.

2207 is prime.

2213 is prime.

2221 is prime.

2237 is prime.

2239 is prime.

2243 is prime.

2251 is prime.

2267 is prime.

2269 is prime.

2273 is prime.

2281 is prime.

2287 is prime.

2293 is prime.

2297 is prime.

2309 is prime.

2311 is prime.

2333 is prime.

2339 is prime.

2341 is prime.

2347 is prime.

2351 is prime.

2357 is prime.

2371 is prime.

2377 is prime.

2381 is prime.

2383 is prime.

2389 is prime.

2393 is prime.

2399 is prime.

2411 is prime.

2417 is prime.

2423 is prime.

2437 is prime.

2441 is prime.

2447 is prime.

2459 is prime.

2467 is prime.

2473 is prime.

2477 is prime.

2503 is prime.

2521 is prime.

2531 is prime.

2539 is prime.

2543 is prime.

2549 is prime.

2551 is prime.

2557 is prime.

2579 is prime.

2591 is prime.

2593 is prime.

2609 is prime.

2617 is prime.

2621 is prime.

2633 is prime.

2647 is prime.

2657 is prime.

2659 is prime.

2663 is prime.

2671 is prime.

2677 is prime.

2683 is prime.

2687 is prime.

2689 is prime.

2693 is prime.

2699 is prime.

2707 is prime.

2711 is prime.

2713 is prime.

2719 is prime.

2729 is prime.

2731 is prime.

2741 is prime.

2749 is prime.

2753 is prime.

2767 is prime.

2777 is prime.

2789 is prime.

2791 is prime.

2797 is prime.

2801 is prime.

2803 is prime.

2819 is prime.

2833 is prime.

2837 is prime.

2843 is prime.

2851 is prime.

2857 is prime.

2861 is prime.

2879 is prime.

2887 is prime.

2897 is prime.

2903 is prime.

2909 is prime.

2917 is prime.

2927 is prime.

2939 is prime.

2953 is prime.

2957 is prime.

2963 is prime.

2969 is prime.

2971 is prime.

2999 is prime.

3001 is prime.

3011 is prime.

3019 is prime.

3023 is prime.

3037 is prime.

3041 is prime.

3049 is prime.

3061 is prime.

3067 is prime.

3079 is prime.

3083 is prime.

3089 is prime.

3109 is prime.

3119 is prime.

3121 is prime.

3137 is prime.

3163 is prime.

3167 is prime.

3169 is prime.

3181 is prime.

3187 is prime.

3191 is prime.

3203 is prime.

3209 is prime.

3217 is prime.

3221 is prime.

3229 is prime.

3251 is prime.

3253 is prime.

3257 is prime.

3259 is prime.

3271 is prime.

3299 is prime.

3301 is prime.

3307 is prime.

3313 is prime.

3319 is prime.

3323 is prime.

3329 is prime.

3331 is prime.

3343 is prime.

3347 is prime.

3359 is prime.

3361 is prime.

3371 is prime.

3373 is prime.

3389 is prime.

3391 is prime.

3407 is prime.

3413 is prime.

3433 is prime.

3449 is prime.

3457 is prime.

3461 is prime.

3463 is prime.

3467 is prime.

3469 is prime.

3491 is prime.

3499 is prime.

3511 is prime.

3517 is prime.

3527 is prime.

3529 is prime.

3533 is prime.

3539 is prime.

3541 is prime.

3547 is prime.

3557 is prime.

3559 is prime.

3571 is prime.

3581 is prime.

3583 is prime.

3593 is prime.

3607 is prime.

3613 is prime.

3617 is prime.

3623 is prime.

3631 is prime.

3637 is prime.

3643 is prime.

3659 is prime.

3671 is prime.

3673 is prime.

3677 is prime.

3691 is prime.

3697 is prime.

3701 is prime.

3709 is prime.

3719 is prime.

3727 is prime.

3733 is prime.

3739 is prime.

3761 is prime.

3767 is prime.

3769 is prime.

3779 is prime.

3793 is prime.

3797 is prime.

3803 is prime.

3821 is prime.

3823 is prime.

3833 is prime.

3847 is prime.

3851 is prime.

3853 is prime.

3863 is prime.

3877 is prime.

3881 is prime.

3889 is prime.

3907 is prime.

3911 is prime.

3917 is prime.

3919 is prime.

3923 is prime.

3929 is prime.

3931 is prime.

3943 is prime.

3947 is prime.

3967 is prime.

3989 is prime.

4001 is prime.

4003 is prime.

4007 is prime.

4013 is prime.

4019 is prime.

4021 is prime.

4027 is prime.

4049 is prime.

4051 is prime.

4057 is prime.

4073 is prime.

4079 is prime.

4091 is prime.

4093 is prime.

4099 is prime.

4111 is prime.

4127 is prime.

4129 is prime.

4133 is prime.

4139 is prime.

4153 is prime.

4157 is prime.

4159 is prime.

4177 is prime.

4201 is prime.

4211 is prime.

4217 is prime.

4219 is prime.

4229 is prime.

4231 is prime.

4241 is prime.

4243 is prime.

4253 is prime.

4259 is prime.

4261 is prime.

4271 is prime.

4273 is prime.

4283 is prime.

4289 is prime.

4297 is prime.

4327 is prime.

4337 is prime.

4339 is prime.

4349 is prime.

4357 is prime.

4363 is prime.

4373 is prime.

4391 is prime.

4397 is prime.

4409 is prime.

4421 is prime.

4423 is prime.

4441 is prime.

4447 is prime.

4451 is prime.

4457 is prime.

4463 is prime.

4481 is prime.

4483 is prime.

4493 is prime.

4507 is prime.

4513 is prime.

4517 is prime.

4519 is prime.

4523 is prime.

4547 is prime.

4549 is prime.

4561 is prime.

4567 is prime.

4583 is prime.

4591 is prime.

4597 is prime.

4603 is prime.

4621 is prime.

4637 is prime.

4639 is prime.

4643 is prime.

4649 is prime.

4651 is prime.

4657 is prime.

4663 is prime.

4673 is prime.

4679 is prime.

4691 is prime.

4703 is prime.

4721 is prime.

4723 is prime.

4729 is prime.

4733 is prime.

4751 is prime.

4759 is prime.

4783 is prime.

4787 is prime.

4789 is prime.

4793 is prime.

4799 is prime.

4801 is prime.

4813 is prime.

4817 is prime.

4831 is prime.

4861 is prime.

4871 is prime.

4877 is prime.

4889 is prime.

4903 is prime.

4909 is prime.

4919 is prime.

4931 is prime.

4933 is prime.

4937 is prime.

4943 is prime.

4951 is prime.

4957 is prime.

4967 is prime.

4969 is prime.

4973 is prime.

4987 is prime.

4993 is prime.

4999 is prime.

5003 is prime.

5009 is prime.

5011 is prime.

5021 is prime.

5023 is prime.

5039 is prime.

5051 is prime.

5059 is prime.

5077 is prime.

5081 is prime.

5087 is prime.

5099 is prime.

5101 is prime.

5107 is prime.

5113 is prime.

5119 is prime.

5147 is prime.

5153 is prime.

5167 is prime.

5171 is prime.

5179 is prime.

5189 is prime.

5197 is prime.

5209 is prime.

5227 is prime.

5231 is prime.

5233 is prime.

5237 is prime.

5261 is prime.

5273 is prime.

5279 is prime.

5281 is prime.

5297 is prime.

5303 is prime.

5309 is prime.

5323 is prime.

5333 is prime.

5347 is prime.

5351 is prime.

5381 is prime.

5387 is prime.

5393 is prime.

5399 is prime.

5407 is prime.

5413 is prime.

5417 is prime.

5419 is prime.

5431 is prime.

5437 is prime.

5441 is prime.

5443 is prime.

5449 is prime.

5471 is prime.

5477 is prime.

5479 is prime.

5483 is prime.

5501 is prime.

5503 is prime.

5507 is prime.

5519 is prime.

5521 is prime.

5527 is prime.

5531 is prime.

5557 is prime.

5563 is prime.

5569 is prime.

5573 is prime.

5581 is prime.

5591 is prime.

5623 is prime.

5639 is prime.

5641 is prime.

5647 is prime.

5651 is prime.

5653 is prime.

5657 is prime.

5659 is prime.

5669 is prime.

5683 is prime.

5689 is prime.

5693 is prime.

5701 is prime.

5711 is prime.

5717 is prime.

5737 is prime.

5741 is prime.

5743 is prime.

5749 is prime.

5779 is prime.

5783 is prime.

5791 is prime.

5801 is prime.

5807 is prime.

5813 is prime.

5821 is prime.

5827 is prime.

5839 is prime.

5843 is prime.

5849 is prime.

5851 is prime.

5857 is prime.

5861 is prime.

5867 is prime.

5869 is prime.

5879 is prime.

5881 is prime.

5897 is prime.

5903 is prime.

5923 is prime.

5927 is prime.

5939 is prime.

5953 is prime.

5981 is prime.

5987 is prime.

6007 is prime.

6011 is prime.

6029 is prime.

6037 is prime.

6043 is prime.

6047 is prime.

6053 is prime.

6067 is prime.

6073 is prime.

6079 is prime.

6089 is prime.

6091 is prime.

6101 is prime.

6113 is prime.

6121 is prime.

6131 is prime.

6133 is prime.

6143 is prime.

6151 is prime.

6163 is prime.

6173 is prime.

6197 is prime.

6199 is prime.

6203 is prime.

6211 is prime.

6217 is prime.

6221 is prime.

6229 is prime.

6247 is prime.

6257 is prime.

6263 is prime.

6269 is prime.

6271 is prime.

6277 is prime.

6287 is prime.

6299 is prime.

6301 is prime.

6311 is prime.

6317 is prime.

6323 is prime.

6329 is prime.

6337 is prime.

6343 is prime.

6353 is prime.

6359 is prime.

6361 is prime.

6367 is prime.

6373 is prime.

6379 is prime.

6389 is prime.

6397 is prime.

6421 is prime.

6427 is prime.

6449 is prime.

6451 is prime.

6469 is prime.

6473 is prime.

6481 is prime.

6491 is prime.

6521 is prime.

6529 is prime.

6547 is prime.

6551 is prime.

6553 is prime.

6563 is prime.

6569 is prime.

6571 is prime.

6577 is prime.

6581 is prime.

6599 is prime.

6607 is prime.

6619 is prime.

6637 is prime.

6653 is prime.

6659 is prime.

6661 is prime.

6673 is prime.

6679 is prime.

6689 is prime.

6691 is prime.

6701 is prime.

6703 is prime.

6709 is prime.

6719 is prime.

6733 is prime.

6737 is prime.

6761 is prime.

6763 is prime.

6779 is prime.

6781 is prime.

6791 is prime.

6793 is prime.

6803 is prime.

6823 is prime.

6827 is prime.

6829 is prime.

6833 is prime.

6841 is prime.

6857 is prime.

6863 is prime.

6869 is prime.

6871 is prime.

6883 is prime.

6899 is prime.

6907 is prime.

6911 is prime.

6917 is prime.

6947 is prime.

6949 is prime.

6959 is prime.

6961 is prime.

6967 is prime.

6971 is prime.

6977 is prime.

6983 is prime.

6991 is prime.

6997 is prime.

7001 is prime.

7013 is prime.

7019 is prime.

7027 is prime.

7039 is prime.

7043 is prime.

7057 is prime.

7069 is prime.

7079 is prime.

7103 is prime.

7109 is prime.

7121 is prime.

7127 is prime.

7129 is prime.

7151 is prime.

7159 is prime.

7177 is prime.

7187 is prime.

7193 is prime.

7207 is prime.

7211 is prime.

7213 is prime.

7219 is prime.

7229 is prime.

7237 is prime.

7243 is prime.

7247 is prime.

7253 is prime.

7283 is prime.

7297 is prime.

7307 is prime.

7309 is prime.

7321 is prime.

7331 is prime.

7333 is prime.

7349 is prime.

7351 is prime.

7369 is prime.

7393 is prime.

7411 is prime.

7417 is prime.

7433 is prime.

7451 is prime.

7457 is prime.

7459 is prime.

7477 is prime.

7481 is prime.

7487 is prime.

7489 is prime.

7499 is prime.

7507 is prime.

7517 is prime.

7523 is prime.

7529 is prime.

7537 is prime.

7541 is prime.

7547 is prime.

7549 is prime.

7559 is prime.

7561 is prime.

7573 is prime.

7577 is prime.

7583 is prime.

7589 is prime.

7591 is prime.

7603 is prime.

7607 is prime.

7621 is prime.

7639 is prime.

7643 is prime.

7649 is prime.

7669 is prime.

7673 is prime.

7681 is prime.

7687 is prime.

7691 is prime.

7699 is prime.

7703 is prime.

7717 is prime.

7723 is prime.

7727 is prime.

7741 is prime.

7753 is prime.

7757 is prime.

7759 is prime.

7789 is prime.

7793 is prime.

7817 is prime.

7823 is prime.

7829 is prime.

7841 is prime.

7853 is prime.

7867 is prime.

7873 is prime.

7877 is prime.

7879 is prime.

7883 is prime.

7901 is prime.

7907 is prime.

7919 is prime.

7927 is prime.

7933 is prime.

7937 is prime.

7949 is prime.

7951 is prime.

7963 is prime.

7993 is prime.

8009 is prime.

8011 is prime.

8017 is prime.

8039 is prime.

8053 is prime.

8059 is prime.

8069 is prime.

8081 is prime.

8087 is prime.

8089 is prime.

8093 is prime.

8101 is prime.

8111 is prime.

8117 is prime.

8123 is prime.

8147 is prime.

8161 is prime.

8167 is prime.

8171 is prime.

8179 is prime.

8191 is prime.

8209 is prime.

8219 is prime.

8221 is prime.

8231 is prime.

8233 is prime.

8237 is prime.

8243 is prime.

8263 is prime.

8269 is prime.

8273 is prime.

8287 is prime.

8291 is prime.

8293 is prime.

8297 is prime.

8311 is prime.

8317 is prime.

8329 is prime.

8353 is prime.

8363 is prime.

8369 is prime.

8377 is prime.

8387 is prime.

8389 is prime.

8419 is prime.

8423 is prime.

8429 is prime.

8431 is prime.

8443 is prime.

8447 is prime.

8461 is prime.

8467 is prime.

8501 is prime.

8513 is prime.

8521 is prime.

8527 is prime.

8537 is prime.

8539 is prime.

8543 is prime.

8563 is prime.

8573 is prime.

8581 is prime.

8597 is prime.

8599 is prime.

8609 is prime.

8623 is prime.

8627 is prime.

8629 is prime.

8641 is prime.

8647 is prime.

8663 is prime.

8669 is prime.

8677 is prime.

8681 is prime.

8689 is prime.

8693 is prime.

8699 is prime.

8707 is prime.

8713 is prime.

8719 is prime.

8731 is prime.

8737 is prime.

8741 is prime.

8747 is prime.

8753 is prime.

8761 is prime.

8779 is prime.

8783 is prime.

8803 is prime.

8807 is prime.

8819 is prime.

8821 is prime.

8831 is prime.

8837 is prime.

8839 is prime.

8849 is prime.

8861 is prime.

8863 is prime.

8867 is prime.

8887 is prime.

8893 is prime.

8923 is prime.

8929 is prime.

8933 is prime.

8941 is prime.

8951 is prime.

8963 is prime.

8969 is prime.

8971 is prime.

8999 is prime.

9001 is prime.

9007 is prime.

9011 is prime.

9013 is prime.

9029 is prime.

9041 is prime.

9043 is prime.

9049 is prime.

9059 is prime.

9067 is prime.

9091 is prime.

9103 is prime.

9109 is prime.

9127 is prime.

9133 is prime.

9137 is prime.

9151 is prime.

9157 is prime.

9161 is prime.

9173 is prime.

9181 is prime.

9187 is prime.

9199 is prime.

9203 is prime.

9209 is prime.

9221 is prime.

9227 is prime.

9239 is prime.

9241 is prime.

9257 is prime.

9277 is prime.

9281 is prime.

9283 is prime.

9293 is prime.

9311 is prime.

9319 is prime.

9323 is prime.

9337 is prime.

9341 is prime.

9343 is prime.

9349 is prime.

9371 is prime.

9377 is prime.

9391 is prime.

9397 is prime.

9403 is prime.

9413 is prime.

9419 is prime.

9421 is prime.

9431 is prime.

9433 is prime.

9437 is prime.

9439 is prime.

9461 is prime.

9463 is prime.

9467 is prime.

9473 is prime.

9479 is prime.

9491 is prime.

9497 is prime.

9511 is prime.

9521 is prime.

9533 is prime.

9539 is prime.

9547 is prime.

9551 is prime.

9587 is prime.

9601 is prime.

9613 is prime.

9619 is prime.

9623 is prime.

9629 is prime.

9631 is prime.

9643 is prime.

9649 is prime.

9661 is prime.

9677 is prime.

9679 is prime.

9689 is prime.

9697 is prime.

9719 is prime.

9721 is prime.

9733 is prime.

9739 is prime.

9743 is prime.

9749 is prime.

9767 is prime.

9769 is prime.

9781 is prime.

9787 is prime.

9791 is prime.

9803 is prime.

9811 is prime.

9817 is prime.

9829 is prime.

9833 is prime.

9839 is prime.

9851 is prime.

9857 is prime.

9859 is prime.

9871 is prime.

9883 is prime.

9887 is prime.

9901 is prime.

9907 is prime.

9923 is prime.

9929 is prime.

9931 is prime.

9941 is prime.

9949 is prime.

9967 is prime.

9973 is prime.

2 is prime.

3 is prime.

5 is prime.

7 is prime.

11 is prime.

13 is prime.

17 is prime.

19 is prime.

23 is prime.

29 is prime.

31 is prime.

37 is prime.

41 is prime.

43 is prime.

47 is prime.

53 is prime.

59 is prime.

61 is prime.

67 is prime.

71 is prime.

73 is prime.

79 is prime.

83 is prime.

89 is prime.

97 is prime.

101 is prime.

103 is prime.

107 is prime.

109 is prime.

113 is prime.

127 is prime.

131 is prime.

137 is prime.

139 is prime.

149 is prime.

151 is prime.

157 is prime.

163 is prime.

167 is prime.

173 is prime.

179 is prime.

181 is prime.

191 is prime.

193 is prime.

197 is prime.

199 is prime.

211 is prime.

223 is prime.

227 is prime.

229 is prime.

233 is prime.

239 is prime.

241 is prime.

251 is prime.

257 is prime.

263 is prime.

269 is prime.

271 is prime.

277 is prime.

281 is prime.

283 is prime.

293 is prime.

307 is prime.

311 is prime.

313 is prime.

317 is prime.

331 is prime.

337 is prime.

347 is prime.

349 is prime.

353 is prime.

359 is prime.

367 is prime.

373 is prime.

379 is prime.

383 is prime.

389 is prime.

397 is prime.

401 is prime.

409 is prime.

419 is prime.

421 is prime.

431 is prime.

433 is prime.

439 is prime.

443 is prime.

449 is prime.

457 is prime.

461 is prime.

463 is prime.

467 is prime.

479 is prime.

487 is prime.

491 is prime.

499 is prime.

503 is prime.

509 is prime.

521 is prime.

523 is prime.

541 is prime.

547 is prime.

557 is prime.

563 is prime.

569 is prime.

571 is prime.

577 is prime.

587 is prime.

593 is prime.

599 is prime.

601 is prime.

607 is prime.

613 is prime.

617 is prime.

619 is prime.

631 is prime.

641 is prime.

643 is prime.

647 is prime.

653 is prime.

659 is prime.

661 is prime.

673 is prime.

677 is prime.

683 is prime.

691 is prime.

701 is prime.

709 is prime.

719 is prime.

727 is prime.

733 is prime.

739 is prime.

743 is prime.

751 is prime.

757 is prime.

761 is prime.

769 is prime.

773 is prime.

787 is prime.

797 is prime.

809 is prime.

811 is prime.

821 is prime.

823 is prime.

827 is prime.

829 is prime.

839 is prime.

853 is prime.

857 is prime.

859 is prime.

863 is prime.

877 is prime.

881 is prime.

883 is prime.

887 is prime.

907 is prime.

911 is prime.

919 is prime.

929 is prime.

937 is prime.

941 is prime.

947 is prime.

953 is prime.

967 is prime.

971 is prime.

977 is prime.

983 is prime.

991 is prime.

997 is prime.

1009 is prime.

1013 is prime.

1019 is prime.

1021 is prime.

1031 is prime.

1033 is prime.

1039 is prime.

1049 is prime.

1051 is prime.

1061 is prime.

1063 is prime.

1069 is prime.

1087 is prime.

1091 is prime.

1093 is prime.

1097 is prime.

1103 is prime.

1109 is prime.

1117 is prime.

1123 is prime.

1129 is prime.

1151 is prime.

1153 is prime.

1163 is prime.

1171 is prime.

1181 is prime.

1187 is prime.

1193 is prime.

1201 is prime.

1213 is prime.

1217 is prime.

1223 is prime.

1229 is prime.

1231 is prime.

1237 is prime.

1249 is prime.

1259 is prime.

1277 is prime.

1279 is prime.

1283 is prime.

1289 is prime.

1291 is prime.

1297 is prime.

1301 is prime.

1303 is prime.

1307 is prime.

1319 is prime.

1321 is prime.

1327 is prime.

1361 is prime.

1367 is prime.

1373 is prime.

1381 is prime.

1399 is prime.

1409 is prime.

1423 is prime.

1427 is prime.

1429 is prime.

1433 is prime.

1439 is prime.

1447 is prime.

1451 is prime.

1453 is prime.

1459 is prime.

1471 is prime.

1481 is prime.

1483 is prime.

1487 is prime.

1489 is prime.

1493 is prime.

1499 is prime.

1511 is prime.

1523 is prime.

1531 is prime.

1543 is prime.

1549 is prime.

1553 is prime.

1559 is prime.

1567 is prime.

1571 is prime.

1579 is prime.

1583 is prime.

1597 is prime.

1601 is prime.

1607 is prime.

1609 is prime.

1613 is prime.

1619 is prime.

1621 is prime.

1627 is prime.

1637 is prime.

1657 is prime.

1663 is prime.

1667 is prime.

1669 is prime.

1693 is prime.

1697 is prime.

1699 is prime.

1709 is prime.

1721 is prime.

1723 is prime.

1733 is prime.

1741 is prime.

1747 is prime.

1753 is prime.

1759 is prime.

1777 is prime.

1783 is prime.

1787 is prime.

1789 is prime.

1801 is prime.

1811 is prime.

1823 is prime.

1831 is prime.

1847 is prime.

1861 is prime.

1867 is prime.

1871 is prime.

1873 is prime.

1877 is prime.

1879 is prime.

1889 is prime.

1901 is prime.

1907 is prime.

1913 is prime.

1931 is prime.

1933 is prime.

1949 is prime.

1951 is prime.

1973 is prime.

1979 is prime.

1987 is prime.

1993 is prime.

1997 is prime.

1999 is prime.

2003 is prime.

2011 is prime.

2017 is prime.

2027 is prime.

2029 is prime.

2039 is prime.

2053 is prime.

2063 is prime.

2069 is prime.

2081 is prime.

2083 is prime.

2087 is prime.

2089 is prime.

2099 is prime.

2111 is prime.

2113 is prime.

2129 is prime.

2131 is prime.

2137 is prime.

2141 is prime.

2143 is prime.

2153 is prime.

2161 is prime.

2179 is prime.

2203 is prime.

2207 is prime.

2213 is prime.

2221 is prime.

2237 is prime.

2239 is prime.

2243 is prime.

2251 is prime.

2267 is prime.

2269 is prime.

2273 is prime.

2281 is prime.

2287 is prime.

2293 is prime.

2297 is prime.

2309 is prime.

2311 is prime.

2333 is prime.

2339 is prime.

2341 is prime.

2347 is prime.

2351 is prime.

2357 is prime.

2371 is prime.

2377 is prime.

2381 is prime.

2383 is prime.

2389 is prime.

2393 is prime.

2399 is prime.

2411 is prime.

2417 is prime.

2423 is prime.

2437 is prime.

2441 is prime.

2447 is prime.

2459 is prime.

2467 is prime.

2473 is prime.

2477 is prime.

2503 is prime.

2521 is prime.

2531 is prime.

2539 is prime.

2543 is prime.

2549 is prime.

2551 is prime.

2557 is prime.

2579 is prime.

2591 is prime.

2593 is prime.

2609 is prime.

2617 is prime.

2621 is prime.

2633 is prime.

2647 is prime.

2657 is prime.

2659 is prime.

2663 is prime.

2671 is prime.

2677 is prime.

2683 is prime.

2687 is prime.

2689 is prime.

2693 is prime.

2699 is prime.

2707 is prime.

2711 is prime.

2713 is prime.

2719 is prime.

2729 is prime.

2731 is prime.

2741 is prime.

2749 is prime.

2753 is prime.

2767 is prime.

2777 is prime.

2789 is prime.

2791 is prime.

2797 is prime.

2801 is prime.

2803 is prime.

2819 is prime.

2833 is prime.

2837 is prime.

2843 is prime.

2851 is prime.

2857 is prime.

2861 is prime.

2879 is prime.

2887 is prime.

2897 is prime.

2903 is prime.

2909 is prime.

2917 is prime.

2927 is prime.

2939 is prime.

2953 is prime.

2957 is prime.

2963 is prime.

2969 is prime.

2971 is prime.

2999 is prime.

3001 is prime.

3011 is prime.

3019 is prime.

3023 is prime.

3037 is prime.

3041 is prime.

3049 is prime.

3061 is prime.

3067 is prime.

3079 is prime.

3083 is prime.

3089 is prime.

3109 is prime.

3119 is prime.

3121 is prime.

3137 is prime.

3163 is prime.

3167 is prime.

3169 is prime.

3181 is prime.

3187 is prime.

3191 is prime.

3203 is prime.

3209 is prime.

3217 is prime.

3221 is prime.

3229 is prime.

3251 is prime.

3253 is prime.

3257 is prime.

3259 is prime.

3271 is prime.

3299 is prime.

3301 is prime.

3307 is prime.

3313 is prime.

3319 is prime.

3323 is prime.

3329 is prime.

3331 is prime.

3343 is prime.

3347 is prime.

3359 is prime.

3361 is prime.

3371 is prime.

3373 is prime.

3389 is prime.

3391 is prime.

3407 is prime.

3413 is prime.

3433 is prime.

3449 is prime.

3457 is prime.

3461 is prime.

3463 is prime.

3467 is prime.

3469 is prime.

3491 is prime.

3499 is prime.

3511 is prime.

3517 is prime.

3527 is prime.

3529 is prime.

3533 is prime.

3539 is prime.

3541 is prime.

3547 is prime.

3557 is prime.

3559 is prime.

3571 is prime.

3581 is prime.

3583 is prime.

3593 is prime.

3607 is prime.

3613 is prime.

3617 is prime.

3623 is prime.

3631 is prime.

3637 is prime.

3643 is prime.

3659 is prime.

3671 is prime.

3673 is prime.

3677 is prime.

3691 is prime.

3697 is prime.

3701 is prime.

3709 is prime.

3719 is prime.

3727 is prime.

3733 is prime.

3739 is prime.

3761 is prime.

3767 is prime.

3769 is prime.

3779 is prime.

3793 is prime.

3797 is prime.

3803 is prime.

3821 is prime.

3823 is prime.

3833 is prime.

3847 is prime.

3851 is prime.

3853 is prime.

3863 is prime.

3877 is prime.

3881 is prime.

3889 is prime.

3907 is prime.

3911 is prime.

3917 is prime.

3919 is prime.

3923 is prime.

3929 is prime.

3931 is prime.

3943 is prime.

3947 is prime.

3967 is prime.

3989 is prime.

4001 is prime.

4003 is prime.

4007 is prime.

4013 is prime.

4019 is prime.

4021 is prime.

4027 is prime.

4049 is prime.

4051 is prime.

4057 is prime.

4073 is prime.

4079 is prime.

4091 is prime.

4093 is prime.

4099 is prime.

4111 is prime.

4127 is prime.

4129 is prime.

4133 is prime.

4139 is prime.

4153 is prime.

4157 is prime.

4159 is prime.

4177 is prime.

4201 is prime.

4211 is prime.

4217 is prime.

4219 is prime.

4229 is prime.

4231 is prime.

4241 is prime.

4243 is prime.

4253 is prime.

4259 is prime.

4261 is prime.

4271 is prime.

4273 is prime.

4283 is prime.

4289 is prime.

4297 is prime.

4327 is prime.

4337 is prime.

4339 is prime.

4349 is prime.

4357 is prime.

4363 is prime.

4373 is prime.

4391 is prime.

4397 is prime.

4409 is prime.

4421 is prime.

4423 is prime.

4441 is prime.

4447 is prime.

4451 is prime.

4457 is prime.

4463 is prime.

4481 is prime.

4483 is prime.

4493 is prime.

4507 is prime.

4513 is prime.

4517 is prime.

4519 is prime.

4523 is prime.

4547 is prime.

4549 is prime.

4561 is prime.

4567 is prime.

4583 is prime.

4591 is prime.

4597 is prime.

4603 is prime.

4621 is prime.

4637 is prime.

4639 is prime.

4643 is prime.

4649 is prime.

4651 is prime.

4657 is prime.

4663 is prime.

4673 is prime.

4679 is prime.

4691 is prime.

4703 is prime.

4721 is prime.

4723 is prime.

4729 is prime.

4733 is prime.

4751 is prime.

4759 is prime.

4783 is prime.

4787 is prime.

4789 is prime.

4793 is prime.

4799 is prime.

4801 is prime.

4813 is prime.

4817 is prime.

4831 is prime.

4861 is prime.

4871 is prime.

4877 is prime.

4889 is prime.

4903 is prime.

4909 is prime.

4919 is prime.

4931 is prime.

4933 is prime.

4937 is prime.

4943 is prime.

4951 is prime.

4957 is prime.

4967 is prime.

4969 is prime.

4973 is prime.

4987 is prime.

4993 is prime.

4999 is prime.

5003 is prime.

5009 is prime.

5011 is prime.

5021 is prime.

5023 is prime.

5039 is prime.

5051 is prime.

5059 is prime.

5077 is prime.

5081 is prime.

5087 is prime.

5099 is prime.

5101 is prime.

5107 is prime.

5113 is prime.

5119 is prime.

5147 is prime.

5153 is prime.

5167 is prime.

5171 is prime.

5179 is prime.

5189 is prime.

5197 is prime.

5209 is prime.

5227 is prime.

5231 is prime.

5233 is prime.

5237 is prime.

5261 is prime.

5273 is prime.

5279 is prime.

5281 is prime.

5297 is prime.

5303 is prime.

5309 is prime.

5323 is prime.

5333 is prime.

5347 is prime.

5351 is prime.

5381 is prime.

5387 is prime.

5393 is prime.

5399 is prime.

5407 is prime.

5413 is prime.

5417 is prime.

5419 is prime.

5431 is prime.

5437 is prime.

5441 is prime.

5443 is prime.

5449 is prime.

5471 is prime.

5477 is prime.

5479 is prime.

5483 is prime.

5501 is prime.

5503 is prime.

5507 is prime.

5519 is prime.

5521 is prime.

5527 is prime.

5531 is prime.

5557 is prime.

5563 is prime.

5569 is prime.

5573 is prime.

5581 is prime.

5591 is prime.

5623 is prime.

5639 is prime.

5641 is prime.

5647 is prime.

5651 is prime.

5653 is prime.

5657 is prime.

5659 is prime.

5669 is prime.

5683 is prime.

5689 is prime.

5693 is prime.

5701 is prime.

5711 is prime.

5717 is prime.

5737 is prime.

5741 is prime.

5743 is prime.

5749 is prime.

5779 is prime.

5783 is prime.

5791 is prime.

5801 is prime.

5807 is prime.

5813 is prime.

5821 is prime.

5827 is prime.

5839 is prime.

5843 is prime.

5849 is prime.

5851 is prime.

5857 is prime.

5861 is prime.

5867 is prime.

5869 is prime.

5879 is prime.

5881 is prime.

5897 is prime.

5903 is prime.

5923 is prime.

5927 is prime.

5939 is prime.

5953 is prime.

5981 is prime.

5987 is prime.

6007 is prime.

6011 is prime.

6029 is prime.

6037 is prime.

6043 is prime.

6047 is prime.

6053 is prime.

6067 is prime.

6073 is prime.

6079 is prime.

6089 is prime.

6091 is prime.

6101 is prime.

6113 is prime.

6121 is prime.

6131 is prime.

6133 is prime.

6143 is prime.

6151 is prime.

6163 is prime.

6173 is prime.

6197 is prime.

6199 is prime.

6203 is prime.

6211 is prime.

6217 is prime.

6221 is prime.

6229 is prime.

6247 is prime.

6257 is prime.

6263 is prime.

6269 is prime.

6271 is prime.

6277 is prime.

6287 is prime.

6299 is prime.

6301 is prime.

6311 is prime.

6317 is prime.

6323 is prime.

6329 is prime.

6337 is prime.

6343 is prime.

6353 is prime.

6359 is prime.

6361 is prime.

6367 is prime.

6373 is prime.

6379 is prime.

6389 is prime.

6397 is prime.

6421 is prime.

6427 is prime.

6449 is prime.

6451 is prime.

6469 is prime.

6473 is prime.

6481 is prime.

6491 is prime.

6521 is prime.

6529 is prime.

6547 is prime.

6551 is prime.

6553 is prime.

6563 is prime.

6569 is prime.

6571 is prime.

6577 is prime.

6581 is prime.

6599 is prime.

6607 is prime.

6619 is prime.

6637 is prime.

6653 is prime.

6659 is prime.

6661 is prime.

6673 is prime.

6679 is prime.

6689 is prime.

6691 is prime.

6701 is prime.

6703 is prime.

6709 is prime.

6719 is prime.

6733 is prime.

6737 is prime.

6761 is prime.

6763 is prime.

6779 is prime.

6781 is prime.

6791 is prime.

6793 is prime.

6803 is prime.

6823 is prime.

6827 is prime.

6829 is prime.

6833 is prime.

6841 is prime.

6857 is prime.

6863 is prime.

6869 is prime.

6871 is prime.

6883 is prime.

6899 is prime.

6907 is prime.

6911 is prime.

6917 is prime.

6947 is prime.

6949 is prime.

6959 is prime.

6961 is prime.

6967 is prime.

6971 is prime.

6977 is prime.

6983 is prime.

6991 is prime.

6997 is prime.

7001 is prime.

7013 is prime.

7019 is prime.

7027 is prime.

7039 is prime.

7043 is prime.

7057 is prime.

7069 is prime.

7079 is prime.

7103 is prime.

7109 is prime.

7121 is prime.

7127 is prime.

7129 is prime.

7151 is prime.

7159 is prime.

7177 is prime.

7187 is prime.

7193 is prime.

7207 is prime.

7211 is prime.

7213 is prime.

7219 is prime.

7229 is prime.

7237 is prime.

7243 is prime.

7247 is prime.

7253 is prime.

7283 is prime.

7297 is prime.

7307 is prime.

7309 is prime.

7321 is prime.

7331 is prime.

7333 is prime.

7349 is prime.

7351 is prime.

7369 is prime.

7393 is prime.

7411 is prime.

7417 is prime.

7433 is prime.

7451 is prime.

7457 is prime.

7459 is prime.

7477 is prime.

7481 is prime.

7487 is prime.

7489 is prime.

7499 is prime.

7507 is prime.

7517 is prime.

7523 is prime.

7529 is prime.

7537 is prime.

7541 is prime.

7547 is prime.

7549 is prime.

7559 is prime.

7561 is prime.

7573 is prime.

7577 is prime.

7583 is prime.

7589 is prime.

7591 is prime.

7603 is prime.

7607 is prime.

7621 is prime.

7639 is prime.

7643 is prime.

7649 is prime.

7669 is prime.

7673 is prime.

7681 is prime.

7687 is prime.

7691 is prime.

7699 is prime.

7703 is prime.

7717 is prime.

7723 is prime.

7727 is prime.

7741 is prime.

7753 is prime.

7757 is prime.

7759 is prime.

7789 is prime.

7793 is prime.

7817 is prime.

7823 is prime.

7829 is prime.

7841 is prime.

7853 is prime.

7867 is prime.

7873 is prime.

7877 is prime.

7879 is prime.

7883 is prime.

7901 is prime.

7907 is prime.

7919 is prime.

7927 is prime.

7933 is prime.

7937 is prime.

7949 is prime.

7951 is prime.

7963 is prime.

7993 is prime.

8009 is prime.

8011 is prime.

8017 is prime.

8039 is prime.

8053 is prime.

8059 is prime.

8069 is prime.

8081 is prime.

8087 is prime.

8089 is prime.

8093 is prime.

8101 is prime.

8111 is prime.

8117 is prime.

8123 is prime.

8147 is prime.

8161 is prime.

8167 is prime.

8171 is prime.

8179 is prime.

8191 is prime.

8209 is prime.

8219 is prime.

8221 is prime.

8231 is prime.

8233 is prime.

8237 is prime.

8243 is prime.

8263 is prime.

8269 is prime.

8273 is prime.

8287 is prime.

8291 is prime.

8293 is prime.

8297 is prime.

8311 is prime.

8317 is prime.

8329 is prime.

8353 is prime.

8363 is prime.

8369 is prime.

8377 is prime.

8387 is prime.

8389 is prime.

8419 is prime.

8423 is prime.

8429 is prime.

8431 is prime.

8443 is prime.

8447 is prime.

8461 is prime.

8467 is prime.

8501 is prime.

8513 is prime.

8521 is prime.

8527 is prime.

8537 is prime.

8539 is prime.

8543 is prime.

8563 is prime.

8573 is prime.

8581 is prime.

8597 is prime.

8599 is prime.

8609 is prime.

8623 is prime.

8627 is prime.

8629 is prime.

8641 is prime.

8647 is prime.

8663 is prime.

8669 is prime.

8677 is prime.

8681 is prime.

8689 is prime.

8693 is prime.

8699 is prime.

8707 is prime.

8713 is prime.

8719 is prime.

8731 is prime.

8737 is prime.

8741 is prime.

8747 is prime.

8753 is prime.

8761 is prime.

8779 is prime.

8783 is prime.

8803 is prime.

8807 is prime.

8819 is prime.

8821 is prime.

8831 is prime.

8837 is prime.

8839 is prime.

8849 is prime.

8861 is prime.

8863 is prime.

8867 is prime.

8887 is prime.

8893 is prime.

8923 is prime.

8929 is prime.

8933 is prime.

8941 is prime.

8951 is prime.

8963 is prime.

8969 is prime.

8971 is prime.

8999 is prime.

9001 is prime.

9007 is prime.

9011 is prime.

9013 is prime.

9029 is prime.

9041 is prime.

9043 is prime.

9049 is prime.

9059 is prime.

9067 is prime.

9091 is prime.

9103 is prime.

9109 is prime.

9127 is prime.

9133 is prime.

9137 is prime.

9151 is prime.

9157 is prime.

9161 is prime.

9173 is prime.

9181 is prime.

9187 is prime.

9199 is prime.

9203 is prime.

9209 is prime.

9221 is prime.

9227 is prime.

9239 is prime.

9241 is prime.

9257 is prime.

9277 is prime.

9281 is prime.

9283 is prime.

9293 is prime.

9311 is prime.

9319 is prime.

9323 is prime.

9337 is prime.

9341 is prime.

9343 is prime.

9349 is prime.

9371 is prime.

9377 is prime.

9391 is prime.

9397 is prime.

9403 is prime.

9413 is prime.

9419 is prime.

9421 is prime.

9431 is prime.

9433 is prime.

9437 is prime.

9439 is prime.

9461 is prime.

9463 is prime.

9467 is prime.

9473 is prime.

9479 is prime.

9491 is prime.

9497 is prime.

9511 is prime.

9521 is prime.

9533 is prime.

9539 is prime.

9547 is prime.

9551 is prime.

9587 is prime.

9601 is prime.

9613 is prime.

9619 is prime.

9623 is prime.

9629 is prime.

9631 is prime.

9643 is prime.

9649 is prime.

9661 is prime.

9677 is prime.

9679 is prime.

9689 is prime.

9697 is prime.

9719 is prime.

9721 is prime.

9733 is prime.

9739 is prime.

9743 is prime.

9749 is prime.

9767 is prime.

9769 is prime.

9781 is prime.

9787 is prime.

9791 is prime.

9803 is prime.

9811 is prime.

9817 is prime.

9829 is prime.

9833 is prime.

9839 is prime.

9851 is prime.

9857 is prime.

9859 is prime.

9871 is prime.

9883 is prime.

9887 is prime.

9901 is prime.

9907 is prime.

9923 is prime.

9929 is prime.

9931 is prime.

9941 is prime.

9949 is prime.

9967 is prime.

9973 is prime.

אריאל

02-10-2009, 15:01

לורי ניסיון נחמד, אך כפי שרון אמר, אחת הטענות שלך שגויות.

נסו לפרק את הגורם n^4+4 לשני גורמים ולראות מה קורה בעקבות זה..

בהצלחה

נסו לפרק את הגורם n^4+4 לשני גורמים ולראות מה קורה בעקבות זה..

בהצלחה

lori

02-10-2009, 15:18

האם למספר לא ראשוני שמחברים 4 יוצא מספר לא ראשוני כמעט בכל המקרים?

אריאל

02-10-2009, 15:21

כן ו..?

ומה זה "כמעט בכל המקרים" יש אינסוף מקרים שזה קורה, ויש אינסוף מקרים שזה לא קורה..

בכל מקרה אני לא רואה איך זה קשור לכאן

ומה זה "כמעט בכל המקרים" יש אינסוף מקרים שזה קורה, ויש אינסוף מקרים שזה לא קורה..

בכל מקרה אני לא רואה איך זה קשור לכאן

גל_כהן

02-10-2009, 15:46

על פי הזהות של סופי ז'רמן (Sophie Germain Identity) מתקיים :

x^4+4y^4=(x^2+2y^2+2xy)(x^2+2y^2-2xy) ובמקרה הנ"ל :

x=n \ , \ y=1 ולכן :

n^4+4=(n^2+2+2n)(n^2+2-2n) ולאחר סידור :

n^4+4=(n^2+2n+2)(n^2-2n+2).

כעת קל לראות שרק במקרה בו אחד הגורמים הוא ראשוני והגורם השני הוא 1,

המספר כולו הוא ראשוני.

נבדוק מתי הגורם הראשון הוא 1 ומתי הגורם השני הוא 1.

n^2+2n+2=1 \right n=-1, אבל n הוא טבעי, ולכן פתרון זה נפסל.

n^2-2n+2=1 \right n=1 ועבור אפשרות זו מתקבל n^4+4=5,

שהוא כמובן ראשוני.

עבור כל אופציה אחרת מקבלים מכפלה של שני מספרים (ראשוניים או לאו),

ומספר שמתפרק למכפלה של לפחות שני מספרים הוא פריק.

יום טוב :) !

x^4+4y^4=(x^2+2y^2+2xy)(x^2+2y^2-2xy) ובמקרה הנ"ל :

x=n \ , \ y=1 ולכן :

n^4+4=(n^2+2+2n)(n^2+2-2n) ולאחר סידור :

n^4+4=(n^2+2n+2)(n^2-2n+2).

כעת קל לראות שרק במקרה בו אחד הגורמים הוא ראשוני והגורם השני הוא 1,

המספר כולו הוא ראשוני.

נבדוק מתי הגורם הראשון הוא 1 ומתי הגורם השני הוא 1.

n^2+2n+2=1 \right n=-1, אבל n הוא טבעי, ולכן פתרון זה נפסל.

n^2-2n+2=1 \right n=1 ועבור אפשרות זו מתקבל n^4+4=5,

שהוא כמובן ראשוני.

עבור כל אופציה אחרת מקבלים מכפלה של שני מספרים (ראשוניים או לאו),

ומספר שמתפרק למכפלה של לפחות שני מספרים הוא פריק.

יום טוב :) !

אריאל

02-10-2009, 15:55

פתרון מדויק גל !

אגב לפירוק שרשמת ניתן להגיע על ידי :

n^4+4=n^4+4n^2+4-4n^2=(n^2+2)^2-(2n)^2=[(n^2+2)+2n)][(n^2+2)-2n]=(n^2+2n+2)(n^2-2n+2)

אגב לפירוק שרשמת ניתן להגיע על ידי :

n^4+4=n^4+4n^2+4-4n^2=(n^2+2)^2-(2n)^2=[(n^2+2)+2n)][(n^2+2)-2n]=(n^2+2n+2)(n^2-2n+2)

גל_כהן

02-10-2009, 16:43

אריאל, זה בדיוק הרעיון בזהות של סופי ז'רמן...

יום טוב :) !

יום טוב :) !

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