我發現了質數有一個規律,請幫我驗算一下

2009-12-15 5:11 am
我發現了質數有一個規律,請幫我驗算一下
nxn-n-1=質數(個位數是3or8除外)
更新1:

sorry, 我打錯,應該係nxn-n+1(個位數是3or8除外)

回答 (2)

2009-12-15 5:55 am
✔ 最佳答案
我幫你驗算過了,在 n <= 50 這個範圍內,除了1, 2, 及個位是3或8外,還有很多不是質數的, 如下:
15 : 11 x 19
19 : 11 x 31
24 : 19 x 29
26 : 11 x 59
30 : 11 x 79
34 : 19 x 59
35 : 29 x 41
37 : 11 x 11 x 11
41 : 11 x 149
44 : 31 x 61
50 : 31 x 79

2009-12-18 20:29:22 補充:
nxn-n+1比nxn+n-1有更多非質數:
5x5-5+1 = 21 = 3x7
8x8-8+1 = 57 = 3x19
10x10-10+1 = 91 = 7x13
11x11-11+1 = 111 = 3x37
12x12-12+1 = 133 = 7x19
14x14-14+1 = 183 = 3x61
17x17-17+1 = 273 = 3x7x13
19x19-19+1 = 343 = 7x7x7
20x20-20+1 = 381 = 3x127...
2009-12-15 5:22 am
When n=1 n^2-n-1=-1 , it is not prime
When n=2 n^2-n-1=1 , it is not prime
If 1,2 are excluded , it seems to be correct
but you may keep going to check more numbers , especially the prime numbers.
參考: by myself


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