趣味素数欣赏

yangchuanju · 发表于 2021-9-6 16:41

趣味素数欣赏
本文素数摘自网页《Prime Patterns》，网址：http://www.magic-squares.net/primes.htm

（一）阶乘和差素数Primes from Factorials !

yangchuanju · 发表于 2021-9-6 16:51

本帖最后由 yangchuanju 于 2021-9-6 16:53 编辑

（二）素数和素数PRIME is Prime
5或7个素数的和是一个素数

更多的素数和素数

yangchuanju · 发表于 2021-9-6 16:59

本帖最后由 yangchuanju 于 2021-9-6 18:35 编辑

（三）各位数字几乎重复的素数Near Repdigit Primes

1800个3+1以内的素数：17个3+1,39个3+1,783个3+1,1731个3+1。

Known (probable) prime numbers
1. (10^2-7)/3 = 31 is prime.
2. (10^3-7)/3 = 331 is prime.
3. (10^4-7)/3 = 3331 is prime.
4. (10^5-7)/3 = 33331 is prime.
5. (10^6-7)/3 = 333331 is prime.
6. (10^7-7)/3 = 3333331 is prime.
7. (10^8-7)/3 = 33333331 is prime.
8. (10^18-7)/3 = (3)17 1<18> is prime.【附注】17个3加1，共18位，下同
9. (10^40-7)/3 = (3)39 1<40> is prime.
10. (10^50-7)/3 = (3)49 1<50> is prime.
11. (10^60-7)/3 = (3)59 1<60> is prime.
12. (10^78-7)/3 = (3)77 1<78> is prime.
13. (10^101-7)/3 = (3)100 1<101> is prime. (Chris K. Caldwell)
14. (10^151-7)/3 = (3)150 1<151> is prime. (Chris K. Caldwell)
15. (10^319-7)/3 = (3)318 1<319> is prime. (Chris K. Caldwell)
16. (10^382-7)/3 = (3)381 1<382> is prime. (Chris K. Caldwell)
17. (10^784-7)/3 = (3)783 1<784> is prime. (Chris K. Caldwell)
18. (10^1732-7)/3 = (3)1731 1<1732> is prime. (discovered by: Chris K. Caldwell) (certified by: Tyler Cadigan / PRIMO 2.2.0 beta 6 / July 27, 2006 )
19. (10^1918-7)/3 = (3)1917 1<1918> is prime. (discovered by: Jason Earls) (certified by: Harvey Dubner / Water, Primo / April 5, 2001 )
20. (10^8855-7)/3 = (3)8854 1<8855> is PRP. (Makoto Kamada / PFGW / February 5, 2004 )
21. (10^11245-7)/3 = (3)11244 1<11245> is PRP. (Daniel Heuer / May 2002 )
22. (10^11960-7)/3 = (3)11959 1<11960> is PRP. (Daniel Heuer / May 2002 )
23. (10^12130-7)/3 = (3)12129 1<12130> is PRP. (Daniel Heuer / May 2002 )
24. (10^18533-7)/3 = (3)18532 1<18533> is PRP. (Makoto Kamada / PFGW / February 6, 2004 )
25. (10^22718-7)/3 = (3)22717 1<22718> is PRP. (Makoto Kamada / PFGW / February 6, 2004 )
26. (10^23365-7)/3 = (3)23364 1<23365> is PRP. (Makoto Kamada / PFGW / February 7, 2004 )
27. (10^24253-7)/3 = (3)24252 1<24253> is PRP. (Makoto Kamada / PFGW / February 7, 2004 )
28. (10^24549-7)/3 = (3)24548 1<24549> is PRP. (Makoto Kamada / PFGW / February 7, 2004 )
29. (10^25324-7)/3 = (3)25323 1<25324> is PRP. (Makoto Kamada / PFGW / February 7, 2004 )
30. (10^30178-7)/3 = (3)30177 1<30178> is PRP. (Makoto Kamada / PFGW / March 20, 2004 )
31. (10^53718-7)/3 = (3)53717 1<53718> is PRP. (Makoto Kamada / PFGW / October 17, 2004 )
32. (10^380976-7)/3 = (3)380975 1<380976> is PRP. (Leonid Durman / NewPGen, PFGW / January 10, 2012 )
33. (10^424861-7)/3 = (3)424860 1<424861> is PRP. (Leonid Durman / NewPGen, PFGW / January 9, 2012 )
【附注】网页原文等号前是分式结构，复制、粘贴过程中分式号丢失，现添加上了括号和除号；感谢白新岭老师找出其中的错误！

Known (probable) prime numbers
1. 6×10^0-1 = 5 is prime.
2. 6×10^1-1 = 59 is prime.
3. 6×10^2-1 = 599 is prime.
4. 6×10^4-1 = 59999 is prime.
5. 6×10^5-1 = 599999 is prime.
6. 6×10^7-1 = 59999999 is prime.
7. 6×10^10-1 = 5(9)10<11> is prime.【附注】5加10个9，共11位，下同
8. 6×10^13-1 = 5(9)13<14> is prime.
9. 6×10^22-1 = 5(9)22<23> is prime.
10. 6×10^23-1 = 5(9)23<24> is prime.
11. 6×10^28-1 = 5(9)28<29> is prime.
12. 6×10^34-1 = 5(9)34<35> is prime.
13. 6×10^40-1 = 5(9)40<41> is prime.
14. 6×10^61-1 = 5(9)61<62> is prime.
15. 6×10^73-1 = 5(9)73<74> is prime.
16. 6×10^361-1 = 5(9)361<362> is prime.
17. 6×10^490-1 = 5(9)490<491> is prime.
18. 6×10^613-1 = 5(9)613<614> is prime.
19. 6×10^1624-1 = 5(9)1624<1625> is prime.
20. 6×10^2000-1 = 5(9)2000<2001> is prime.
21. 6×10^2994-1 = 5(9)2994<2995> is prime.
22. 6×10^4301-1 = 5(9)4301<4302> is prime. (Harvey Dubner / Cruncher / December 31, 1988 )
23. 6×10^4332-1 = 5(9)4332<4333> is prime. (Harvey Dubner / Cruncher / December 31, 1988 )
24. 6×10^18668-1 = 5(9)18668<18669> is prime. (Ray Ballinger / OpenPFGW / February 22, 2000 )
25. 6×10^32544-1 = 5(9)32544<32545> is prime. (Eric J. Sorensen / Proth.exe / September 26, 2001 )
26. 6×10^34936-1 = 5(9)34936<34937> is prime. (Eric J. Sorensen / Proth.exe / September 30, 2001 )
27. 6×10^267598-1 = 5(9)267598<267599> is prime. (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 15, 2010 )
28. 6×10^270658-1 = 5(9)270658<270659> is prime. (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 19, 2010 )
29. 6×10^293134-1 = 5(9)293134<293135> is prime. (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 19, 2010 )
30. 6×10^319889-1 = 5(9)319889<319890> is prime. (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 19, 2010 )
31. 6×10^414508-1 = 5(9)414508<414509> is prime. (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / January 8, 2011 )

yangchuanju · 发表于 2021-9-6 17:18

（四）最小、最大素数Smallest & Largest Primes

yangchuanju · 发表于 2021-9-6 18:41

（五）三个连续的5,7,9位素数和还是一个同位素数

yangchuanju · 发表于 2021-9-6 18:49

（六）回文素数Palindromic Primes

yangchuanju · 发表于 2021-9-6 18:58

（七）可逆素数Reversible Primes

（八）连续间隙素数Consecutive gaps ... primes

yangchuanju · 发表于 2021-9-6 19:01

（九）阶梯素数

重生888@ · 发表于 2021-9-6 22:18

为楼主点赞！点赞！

yangchuanju · 发表于 2021-9-7 09:05

（十）4、5、6阶幻方素数
在以下各4阶、5阶、6阶方阵中，将各行、各列及对角线上的4—6数（包括各行、各列及对角线倒着排）合成一个新的数字，这些数字都是素数（相当于幻方之行列及对角线和都等于幻和，但各方阵本身不是幻方）：
4阶方阵：
1 1 9 3
9 2 5 7
3 8 5 1
3 3 1 9

位置正排倒排
第1行 1193 is prime 3911 is prime
第2行 9257 is prime 7529 is prime
第3行 3851 is prime 1583 is prime
第4行 3319 is prime 9133 is prime
第1列 1933 is prime 3391 is prime
第2列 1283 is prime 3821 is prime
第3列 9551 is prime 1559 is prime
第4列 3719 is prime 9173 is prime
主对角线 1259 is prime 9521 is prime
副对角线 3853 is prime 3583 is prime

5阶方阵：
1 1 7 3 1
7 2 2 5 1
3 1 8 5 9
9 0 7 9 3
3 9 1 1 3

位置正排倒排
第1行 11731 is prime 13711 is prime
第2行 72251 is prime 15227 is prime
第3行 31859 is prime 95813 is prime
第4行 90793 is prime 39709 is prime
第5行 39113 is prime 31193 is prime
第1列 17393 is prime 39371 is prime
第2列 12109 is prime 90121 is prime
第3列 72871 is prime 17827 is prime
第4列 35591 is prime 19553 is prime
第5列 11933 is prime 33911 is prime
主对角线 12893 is prime 39821 is prime
副对角线 30851 is prime 15803 is prime

		自动登录	找回密码
密码			注册

趣味素数欣赏

本帖子中包含更多资源

本帖子中包含更多资源

本帖子中包含更多资源

点评

本帖子中包含更多资源

点评

本帖子中包含更多资源

本帖子中包含更多资源

本帖子中包含更多资源

本帖子中包含更多资源

点评