20200614, 10:51  #815  
Nov 2016
5·571 Posts 
Quote:
Corrected: R96 has some k proven composite by partial algebra factors 

20200617, 17:25  #816 
Nov 2016
101100100111_{2} Posts 
the conjectured first 4 Sierpinski/Riesel numbers for bases up to 256

20200618, 19:37  #817  
Nov 2016
5×571 Posts 
Quote:
If there are at least two primes of the form (k*b^n+c)/gcd(k+c, b1) (k>=1, b>=2, c != 0, gcd(k,c)=1, gcd(b,c)=1) with n>=1, then (k*b^n+c)/gcd(k+c, b1) has no covering set. Strong conjecture: If there are at least two primes of the form (k*b^n+c)/gcd(k+c, b1) (k>=1, b>=2, c != 0, gcd(k,c)=1, gcd(b,c)=1) with n>=1, then (k*b^n+c)/gcd(k+c, b1) satisfies step 3 (i.e. does not make a full covering set with (all primes), (all algebraic factors), or (partial primes, partial algebraic factors). (note that this is not true when there is only one such prime, counterexamples: (1*4^n1)/gcd(11,41), (1*8^n1)/gcd(11,81), (1*16^n1)/gcd(11,161), (1*36^n1)/gcd(11,361), (27*8^n+1)/gcd(27+1,81), ...) If the strong conjecture and the conjecture in post #783 are both true, then: If there are at least two primes of the form (k*b^n+c)/gcd(k+c, b1) (k>=1, b>=2, c != 0, gcd(k,c)=1, gcd(b,c)=1) with n>=1, then there are infinitely many primes of this form. 

20200619, 09:06  #818 
Nov 2016
5×571 Posts 
Stronger conjectures: (assuming k is positive integer)
* if k < 78557, then there are infinitely many primes of the form (k*2^n+1)/gcd(k+1,21) with integer n>=1 * if k < 11047, then there are infinitely many primes of the form (k*3^n+1)/gcd(k+1,31) with integer n>=1 * if k < 419, then there are infinitely many primes of the form (k*4^n+1)/gcd(k+1,41) with integer n>=1 * if k < 7, then there are infinitely many primes of the form (k*5^n+1)/gcd(k+1,51) with integer n>=1 * if k < 174308, then there are infinitely many primes of the form (k*6^n+1)/gcd(k+1,61) with integer n>=1 * if k < 209, then there are infinitely many primes of the form (k*7^n+1)/gcd(k+1,71) with integer n>=1 * if k < 47, then there are infinitely many primes of the form (k*8^n+1)/gcd(k+1,81) with integer n>=1 * if k < 31, then there are infinitely many primes of the form (k*9^n+1)/gcd(k+1,91) with integer n>=1 * if k < 989, then there are infinitely many primes of the form (k*10^n+1)/gcd(k+1,101) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*11^n+1)/gcd(k+1,111) with integer n>=1 * if k < 521, then there are infinitely many primes of the form (k*12^n+1)/gcd(k+1,121) with integer n>=1 * if k < 15, then there are infinitely many primes of the form (k*13^n+1)/gcd(k+1,131) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*14^n+1)/gcd(k+1,141) with integer n>=1 * if k < 673029, then there are infinitely many primes of the form (k*15^n+1)/gcd(k+1,151) with integer n>=1 * if k < 38, then there are infinitely many primes of the form (k*16^n+1)/gcd(k+1,161) with integer n>=1 * if k < 31, then there are infinitely many primes of the form (k*17^n+1)/gcd(k+1,171) with integer n>=1 * if k < 398, then there are infinitely many primes of the form (k*18^n+1)/gcd(k+1,181) with integer n>=1 * if k < 9, then there are infinitely many primes of the form (k*19^n+1)/gcd(k+1,191) with integer n>=1 * if k < 8, then there are infinitely many primes of the form (k*20^n+1)/gcd(k+1,201) with integer n>=1 * if k < 23, then there are infinitely many primes of the form (k*21^n+1)/gcd(k+1,211) with integer n>=1 * if k < 2253, then there are infinitely many primes of the form (k*22^n+1)/gcd(k+1,221) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*23^n+1)/gcd(k+1,231) with integer n>=1 * if k < 30651, then there are infinitely many primes of the form (k*24^n+1)/gcd(k+1,241) with integer n>=1 * if k < 79, then there are infinitely many primes of the form (k*25^n+1)/gcd(k+1,251) with integer n>=1 * if k < 221, then there are infinitely many primes of the form (k*26^n+1)/gcd(k+1,261) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*27^n+1)/gcd(k+1,271) with integer n>=1 * if k < 4554, then there are infinitely many primes of the form (k*28^n+1)/gcd(k+1,281) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*29^n+1)/gcd(k+1,291) with integer n>=1 * if k < 867, then there are infinitely many primes of the form (k*30^n+1)/gcd(k+1,301) with integer n>=1 * if k < 239, then there are infinitely many primes of the form (k*31^n+1)/gcd(k+1,311) with integer n>=1 * if k < 10, then there are infinitely many primes of the form (k*32^n+1)/gcd(k+1,321) with integer n>=1 * if k < 511, then there are infinitely many primes of the form (k*33^n+1)/gcd(k+1,331) with integer n>=1 * if k < 6, then there are infinitely many primes of the form (k*34^n+1)/gcd(k+1,341) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*35^n+1)/gcd(k+1,351) with integer n>=1 * if k < 1886, then there are infinitely many primes of the form (k*36^n+1)/gcd(k+1,361) with integer n>=1 * if k < 39, then there are infinitely many primes of the form (k*37^n+1)/gcd(k+1,371) with integer n>=1 * if k < 14, then there are infinitely many primes of the form (k*38^n+1)/gcd(k+1,381) with integer n>=1 * if k < 9, then there are infinitely many primes of the form (k*39^n+1)/gcd(k+1,391) with integer n>=1 * if k < 47723, then there are infinitely many primes of the form (k*40^n+1)/gcd(k+1,401) with integer n>=1 * if k < 8, then there are infinitely many primes of the form (k*41^n+1)/gcd(k+1,411) with integer n>=1 * if k < 13372, then there are infinitely many primes of the form (k*42^n+1)/gcd(k+1,421) with integer n>=1 * if k < 21, then there are infinitely many primes of the form (k*43^n+1)/gcd(k+1,431) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*44^n+1)/gcd(k+1,441) with integer n>=1 * if k < 47, then there are infinitely many primes of the form (k*45^n+1)/gcd(k+1,451) with integer n>=1 * if k < 881, then there are infinitely many primes of the form (k*46^n+1)/gcd(k+1,461) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*47^n+1)/gcd(k+1,471) with integer n>=1 * if k < 1219, then there are infinitely many primes of the form (k*48^n+1)/gcd(k+1,481) with integer n>=1 * if k < 31, then there are infinitely many primes of the form (k*49^n+1)/gcd(k+1,491) with integer n>=1 * if k < 16, then there are infinitely many primes of the form (k*50^n+1)/gcd(k+1,501) with integer n>=1 * if k < 25, then there are infinitely many primes of the form (k*51^n+1)/gcd(k+1,511) with integer n>=1 * if k < 28674, then there are infinitely many primes of the form (k*52^n+1)/gcd(k+1,521) with integer n>=1 * if k < 7, then there are infinitely many primes of the form (k*53^n+1)/gcd(k+1,531) with integer n>=1 * if k < 21, then there are infinitely many primes of the form (k*54^n+1)/gcd(k+1,541) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*55^n+1)/gcd(k+1,551) with integer n>=1 * if k < 20, then there are infinitely many primes of the form (k*56^n+1)/gcd(k+1,561) with integer n>=1 * if k < 47, then there are infinitely many primes of the form (k*57^n+1)/gcd(k+1,571) with integer n>=1 * if k < 488, then there are infinitely many primes of the form (k*58^n+1)/gcd(k+1,581) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*59^n+1)/gcd(k+1,591) with integer n>=1 * if k < 16957, then there are infinitely many primes of the form (k*60^n+1)/gcd(k+1,601) with integer n>=1 * if k < 63, then there are infinitely many primes of the form (k*61^n+1)/gcd(k+1,611) with integer n>=1 * if k < 8, then there are infinitely many primes of the form (k*62^n+1)/gcd(k+1,621) with integer n>=1 * if k < 1589, then there are infinitely many primes of the form (k*63^n+1)/gcd(k+1,631) with integer n>=1 * if k < 14, then there are infinitely many primes of the form (k*64^n+1)/gcd(k+1,641) with integer n>=1 * if k < 509203, then there are infinitely many primes of the form (k*2^n1)/gcd(k1,21) with integer n>=1 * if k < 12119, then there are infinitely many primes of the form (k*3^n1)/gcd(k1,31) with integer n>=1 * if k < 361, then there are infinitely many primes of the form (k*4^n1)/gcd(k1,41) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*5^n1)/gcd(k1,51) with integer n>=1 * if k < 84687, then there are infinitely many primes of the form (k*6^n1)/gcd(k1,61) with integer n>=1 * if k < 457, then there are infinitely many primes of the form (k*7^n1)/gcd(k1,71) with integer n>=1 * if k < 14, then there are infinitely many primes of the form (k*8^n1)/gcd(k1,81) with integer n>=1 * if k < 41, then there are infinitely many primes of the form (k*9^n1)/gcd(k1,91) with integer n>=1 * if k < 334, then there are infinitely many primes of the form (k*10^n1)/gcd(k1,101) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*11^n1)/gcd(k1,111) with integer n>=1 * if k < 376, then there are infinitely many primes of the form (k*12^n1)/gcd(k1,121) with integer n>=1 * if k < 29, then there are infinitely many primes of the form (k*13^n1)/gcd(k1,131) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*14^n1)/gcd(k1,141) with integer n>=1 * if k < 622403, then there are infinitely many primes of the form (k*15^n1)/gcd(k1,151) with integer n>=1 * if k < 100, then there are infinitely many primes of the form (k*16^n1)/gcd(k1,161) with integer n>=1 * if k < 49, then there are infinitely many primes of the form (k*17^n1)/gcd(k1,171) with integer n>=1 * if k < 246, then there are infinitely many primes of the form (k*18^n1)/gcd(k1,181) with integer n>=1 * if k < 9, then there are infinitely many primes of the form (k*19^n1)/gcd(k1,191) with integer n>=1 * if k < 8, then there are infinitely many primes of the form (k*20^n1)/gcd(k1,201) with integer n>=1 * if k < 45, then there are infinitely many primes of the form (k*21^n1)/gcd(k1,211) with integer n>=1 * if k < 2738, then there are infinitely many primes of the form (k*22^n1)/gcd(k1,221) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*23^n1)/gcd(k1,231) with integer n>=1 * if k < 32336, then there are infinitely many primes of the form (k*24^n1)/gcd(k1,241) with integer n>=1 * if k < 105, then there are infinitely many primes of the form (k*25^n1)/gcd(k1,251) with integer n>=1 * if k < 149, then there are infinitely many primes of the form (k*26^n1)/gcd(k1,261) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*27^n1)/gcd(k1,271) with integer n>=1 * if k < 3769, then there are infinitely many primes of the form (k*28^n1)/gcd(k1,281) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*29^n1)/gcd(k1,291) with integer n>=1 * if k < 4928, then there are infinitely many primes of the form (k*30^n1)/gcd(k1,301) with integer n>=1 * if k < 145, then there are infinitely many primes of the form (k*31^n1)/gcd(k1,311) with integer n>=1 * if k < 10, then there are infinitely many primes of the form (k*32^n1)/gcd(k1,321) with integer n>=1 * if k < 545, then there are infinitely many primes of the form (k*33^n1)/gcd(k1,331) with integer n>=1 * if k < 6, then there are infinitely many primes of the form (k*34^n1)/gcd(k1,341) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*35^n1)/gcd(k1,351) with integer n>=1 * if k < 33791, then there are infinitely many primes of the form (k*36^n1)/gcd(k1,361) with integer n>=1 * if k < 29, then there are infinitely many primes of the form (k*37^n1)/gcd(k1,371) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*38^n1)/gcd(k1,381) with integer n>=1 * if k < 9, then there are infinitely many primes of the form (k*39^n1)/gcd(k1,391) with integer n>=1 * if k < 25462, then there are infinitely many primes of the form (k*40^n1)/gcd(k1,401) with integer n>=1 * if k < 8, then there are infinitely many primes of the form (k*41^n1)/gcd(k1,411) with integer n>=1 * if k < 15137, then there are infinitely many primes of the form (k*42^n1)/gcd(k1,421) with integer n>=1 * if k < 21, then there are infinitely many primes of the form (k*43^n1)/gcd(k1,431) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*44^n1)/gcd(k1,441) with integer n>=1 * if k < 93, then there are infinitely many primes of the form (k*45^n1)/gcd(k1,451) with integer n>=1 * if k < 928, then there are infinitely many primes of the form (k*46^n1)/gcd(k1,461) with integer n>=1 * if k < 5, then there are infinitely many primes of the form (k*47^n1)/gcd(k1,471) with integer n>=1 * if k < 3226, then there are infinitely many primes of the form (k*48^n1)/gcd(k1,481) with integer n>=1 * if k < 81, then there are infinitely many primes of the form (k*49^n1)/gcd(k1,491) with integer n>=1 * if k < 16, then there are infinitely many primes of the form (k*50^n1)/gcd(k1,501) with integer n>=1 * if k < 25, then there are infinitely many primes of the form (k*51^n1)/gcd(k1,511) with integer n>=1 * if k < 25015, then there are infinitely many primes of the form (k*52^n1)/gcd(k1,521) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*53^n1)/gcd(k1,531) with integer n>=1 * if k < 21, then there are infinitely many primes of the form (k*54^n1)/gcd(k1,541) with integer n>=1 * if k < 13, then there are infinitely many primes of the form (k*55^n1)/gcd(k1,551) with integer n>=1 * if k < 20, then there are infinitely many primes of the form (k*56^n1)/gcd(k1,561) with integer n>=1 * if k < 144, then there are infinitely many primes of the form (k*57^n1)/gcd(k1,571) with integer n>=1 * if k < 547, then there are infinitely many primes of the form (k*58^n1)/gcd(k1,581) with integer n>=1 * if k < 4, then there are infinitely many primes of the form (k*59^n1)/gcd(k1,591) with integer n>=1 * if k < 20558, then there are infinitely many primes of the form (k*60^n1)/gcd(k1,601) with integer n>=1 * if k < 125, then there are infinitely many primes of the form (k*61^n1)/gcd(k1,611) with integer n>=1 * if k < 8, then there are infinitely many primes of the form (k*62^n1)/gcd(k1,621) with integer n>=1 * if k < 857, then there are infinitely many primes of the form (k*63^n1)/gcd(k1,631) with integer n>=1 * if k < 14, then there are infinitely many primes of the form (k*64^n1)/gcd(k1,641) with integer n>=1 
20200619, 09:25  #819  
Nov 2016
5×571 Posts 
Quote:
* For (k*8^n+1)/gcd(k+1,81), k is not cube of integer * For (k*16^n+1)/gcd(k+1,161), k is not of the form 4*q^4 with integer q * For (k*27^n+1)/gcd(k+1,271), k is not cube of integer * For (k*32^n+1)/gcd(k+1,321), k is not fifth power of integer * For (k*64^n+1)/gcd(k+1,641), k is not cube of integer * For (k*4^n1)/gcd(k1,41), k is not square of integer * For (k*8^n1)/gcd(k1,81), k is not cube of integer * For (k*9^n1)/gcd(k1,91), k is not square of integer * For (k*12^n1)/gcd(k1,121), k is not of the form m^2 with integer m == 5 or 8 mod 13 nor of the form 3*m^2 with integer m == 3 or 10 mod 13 * For (k*16^n1)/gcd(k1,161), k is not square of integer * For (k*19^n1)/gcd(k1,191), k is not of the form m^2 with integer m == 2 or 3 mod 5 * For (k*24^n1)/gcd(k1,241), k is not of the form m^2 with integer m == 2 or 3 mod 5 nor of the form 6*m^2 with integer m == 1 or 4 mod 5 * For (k*25^n1)/gcd(k1,251), k is not square of integer * For (k*27^n1)/gcd(k1,271), k is not cube of integer * For (k*28^n1)/gcd(k1,281), k is not of the form m^2 with integer m == 12 or 17 mod 29 nor of the form 7*m^2 with integer m == 5 or 24 mod 29 * For (k*30^n1)/gcd(k1,301), k is not equal to 1369 * For (k*32^n1)/gcd(k1,321), k is not fifth power of integer * For (k*33^n1)/gcd(k1,331), k is not of the form m^2 with integer m == 4 or 13 mod 17 nor of the form 33*m^2 with integer m == 4 or 13 mod 17 nor of the form m^2 with integer m == 15 or 17 mod 32 * For (k*34^n1)/gcd(k1,341), k is not of the form m^2 with integer m == 2 or 3 mod 5 * For (k*36^n1)/gcd(k1,361), k is not square of integer * For (k*39^n1)/gcd(k1,391), k is not of the form m^2 with integer m == 2 or 3 mod 5 * For (k*40^n1)/gcd(k1,401), k is not of the form m^2 with integer m == 9 or 32 mod 41 nor of the form 10*m^2 with integer m == 18 or 23 mod 41 * For (k*49^n1)/gcd(k1,491), k is not square of integer * For (k*52^n1)/gcd(k1,521), k is not of the form m^2 with integer m == 23 or 30 mod 53 nor of the form 13*m^2 with integer m == 7 or 46 mod 53 * For (k*54^n1)/gcd(k1,541), k is not of the form m^2 with integer m == 2 or 3 mod 5 nor of the form 6*m^2 with integer m == 1 or 4 mod 5 * For (k*57^n1)/gcd(k1,571), k is not of the form m^2 with integer m == 3 or 5 mod 8 * For (k*60^n1)/gcd(k1,601), k is not of the form m^2 with integer m == 11 or 50 mod 61 nor of the form 15*m^2 with integer m == 22 or 39 mod 61 * For (k*64^n1)/gcd(k1,641), k is not square of integer nor cube of integer Last fiddled with by sweety439 on 20200619 at 17:52 

20200619, 17:02  #820  
Nov 2016
5·571 Posts 
Quote:
If k < 4th CK and does not equal to 1st CK, 2nd CK, or 3rd CK, then there are infinitely many primes of the form (k*b^n+1)/gcd(k+1,b1) (+ for Sierpinski,  for Riesel) with integer n>=1 Sierpinski: Code:
b: 1st CK, 2nd CK, 3rd CK, 4th CK 2: 78557, 157114, 271129, 271577, 3: 11047, 23789, 27221, 32549, 4: 419, 659, 794, 1466, 5: 7, 11, 31, 35, 6: 174308, 188299, 243417, 282001, 7: 209, 1463, 3305, 3533, 8: 47, 79, 83, 181, 9: 31, 39, 111, 119, 10: 989, 1121, 3653, 3662, 11: 5, 7, 17, 19, 12: 521, 597, 1143, 1509, 13: 15, 27, 47, 71, 14: 4, 11, 19, 26, 15: 673029, 2105431, 2692337, 4621459, 16: 38, 194, 524, 608, 17: 31, 47, 127, 143, 18: 398, 512, 571, 989, 19: 9, 11, 29, 31, 20: 8, 13, 29, 34, 21: 23, 43, 47, 111, 22: 2253, 4946, 6694, 8417, 23: 5, 7, 17, 19, 24: 30651, 66356, 77554, 84766, 25: 79, 103, 185, 287, 26: 221, 284, 1627, 1766, 27: 13, 15, 41, 43, 28: 4554, 8293, 13687, 18996, 29: 4, 7, 11, 19, 30: 867, 9859, 10386, 10570, 31: 239, 293, 521, 1025, 32: 10, 23, 43, 56, 33: 511, 543, 1599, 1631, 34: 6, 29, 41, 64, 35: 5, 7, 17, 19, 36: 1886, 11093, 67896, 123189, 37: 39, 75, 87, 191, 38: 14, 16, 25, 53, 39: 9, 11, 29, 31, 40: 47723, 67241, 68963, 133538, 41: 8, 13, 15, 23, 42: 13372, 30359, 47301, 60758, 43: 21, 23, 65, 67, 44: 4, 11, 19, 26, 45: 47, 91, 231, 275, 46: 881, 1592, 2519, 3104, 47: 5, 7, 8, 16, 48: 1219, 3403, 5531, 5613, 49: 31, 79, 179, 191, 50: 16, 35, 67, 86, 51: 25, 27, 77, 79, 52: 28674, 57398, 83262, 117396, 53: 7, 11, 31, 35, 54: 21, 34, 76, 89, 55: 13, 15, 41, 43, 56: 20, 37, 77, 94, 57: 47, 175, 231, 311, 58: 488, 1592, 7766, 8312, 59: 4, 5, 7, 9, 60: 16957, 84486, 138776, 199103, 61: 63, 123, 311, 371, 62: 8, 13, 29, 34, 63: 1589, 2381, 4827, 7083, 64: 14, 51, 79, 116, 65: 10, 23, 43, 56, 66: 67: 26, 33, 35, 101, 68: 22, 36, 47, 56, 69: 6, 15, 19, 27, 70: 11077, 20591, 22719, 25914, 71: 5, 7, 17, 19, 72: 731, 1313, 1461, 3724, 73: 47, 223, 255, 295, 74: 4, 11, 19, 26, 75: 37, 39, 113, 115, 76: 34, 43, 111, 120, 77: 7, 11, 14, 25, 78: 96144, 186123, 288507, 390656, 79: 9, 11, 29, 31, 80: 1039, 3181, 7438, 12211, 81: 575, 649, 655, 1167, 82: 19587, 29051, 37847, 46149, 83: 5, 7, 8, 13, 84: 16, 69, 101, 154, 85: 87, 171, 431, 515, 86: 28, 59, 115, 146, 87: 21, 23, 65, 67, 88: 26, 179, 311, 521, 89: 4, 11, 19, 23, 90: 27, 64, 118, 155, 91: 45, 47, 137, 139, 92: 32, 61, 125, 154, 93: 95, 187, 471, 563, 94: 39, 56, 134, 151, 95: 5, 7, 17, 19, 96: 68869, 353081, 426217, 427383, 97: 127, 223, 575, 671, 98: 10, 16, 23, 38, 99: 9, 11, 29, 31, 100: 62, 233, 332, 836, 101: 7, 11, 16, 31, 102: 293, 1342, 6060, 6240, 103: 25, 27, 77, 79, 104: 4, 6, 8, 11, 105: 319, 423, 1167, 1271, 106: 2387, 5480, 14819, 17207, 107: 5, 7, 17, 19, 108: 26270, 102677, 131564, 132872, 109: 19, 21, 23, 31, 110: 38, 73, 149, 184, 111: 13, 15, 41, 43, 112: 2261, 2939, 3502, 5988, 113: 20, 31, 37, 47, 114: 24, 91, 139, 206, 115: 57, 59, 173, 175, 116: 14, 25, 53, 64, 117: 119, 235, 327, 591, 118: 50, 69, 169, 188, 119: 4, 5, 7, 9, 120: 121: 27, 103, 110, 293, 122: 40, 47, 79, 83, 123: 55, 61, 63, 69, 124: 31001, 56531, 77381, 145994, 125: 7, 8, 11, 13, 126: 766700, 1835532, 2781934, 2986533, 127: 6343, 7909, 12923, 13701, 128: 44, 85, 98, 173, 129: 14, 51, 79, 116, 130: 1049, 2432, 7073, 9602, 131: 5, 7, 10, 17, 132: 13, 20, 113, 153, 133: 59, 135, 267, 671, 134: 4, 11, 19, 26, 135: 33, 35, 101, 103, 136: 29180, 90693, 151660, 243037, 137: 22, 23, 31, 47, 138: 2781, 3752, 4308, 7229, 139: 6, 9, 11, 13, 140: 46, 95, 187, 236, 141: 143, 283, 711, 851, 142: 12, 131, 155, 221, 143: 5, 7, 17, 19, 144: 59, 86, 204, 231, 145: 1023, 1167, 2159, 2367, 146: 8, 13, 29, 34, 147: 73, 75, 221, 223, 148: 3128, 4022, 4471, 7749, 149: 4, 7, 11, 19, 150: 49074, 95733, 539673, 611098, 151: 37, 39, 113, 115, 152: 16, 35, 67, 86, 153: 15, 34, 43, 55, 154: 61, 94, 216, 249, 155: 5, 7, 14, 17, 156: 157: 47, 59, 159, 191, 158: 52, 107, 122, 211, 159: 9, 11, 29, 31, 160: 22, 139, 183, 300, 161: 95, 127, 287, 319, 162: 6193, 6682, 7336, 14343, 163: 81, 83, 245, 247, 164: 4, 10, 11, 19, 165: 167, 331, 831, 995, 166: 335, 5510, 7349, 9854, 167: 5, 7, 8, 13, 168: 9244, 9658, 15638, 20357, 169: 16, 31, 39, 69, 170: 20, 37, 77, 94, 171: 85, 87, 257, 259, 172: 62, 108, 836, 1070, 173: 7, 11, 28, 31, 174: 6, 29, 41, 64, 175: 21, 23, 65, 67, 176: 58, 119, 235, 296, 177: 79, 447, 1247, 1423, 178: 569, 797, 953, 1031, 179: 4, 5, 7, 9, 180: 1679679, 181: 15, 27, 51, 64, 182: 23, 62, 121, 211, 183: 45, 47, 69, 101, 184: 36, 149, 221, 269, 185: 23, 31, 32, 61, 186: 67, 120, 254, 307, 187: 47, 83, 93, 95, 188: 8, 13, 29, 34, 189: 19, 31, 39, 56, 190: 2157728, 3146151, 3713039, 4352889, 191: 5, 7, 17, 19, 192: 7879, 8686, 17371, 19494, 193: 2687, 6015, 6207, 9343, 194: 4, 11, 14, 19, 195: 13, 15, 41, 43, 196: 16457, 78689, 86285, 95147, 197: 7, 10, 11, 23, 198: 4105, 19484, 21649, 23581, 199: 9, 11, 29, 31, 200: 47, 68, 103, 118, 201: 607, 807, 2223, 2423, 202: 57, 146, 260, 349, 203: 5, 7, 16, 17, 204: 81, 124, 286, 329, 205: 207, 411, 1031, 1235, 206: 22, 47, 91, 116, 207: 25, 27, 77, 79, 208: 56, 98, 153, 265, 209: 4, 6, 8, 11, 210: 211: 105, 107, 317, 319, 212: 70, 143, 283, 285, 213: 51, 215, 339, 427, 214: 44, 171, 236, 259, 215: 5, 7, 17, 19, 216: 92, 125, 309, 342, 217: 655, 863, 871, 919, 218: 74, 145, 293, 364, 219: 9, 11, 21, 23, 220: 50, 103, 118, 324, 221: 7, 11, 31, 35, 222: 333163, 352341, 389359, 410098, 223: 13, 15, 41, 43, 224: 4, 11, 19, 26, 225: 3391, 3615, 10623, 10847, 226: 2915, 11744, 12563, 15704, 227: 5, 7, 17, 19, 228: 1146, 7098, 8474, 25647, 229: 19, 24, 31, 47, 230: 8, 10, 13, 23, 231: 57, 59, 173, 175, 232: 2564, 18992, 27527, 46520, 233: 14, 23, 25, 31, 234: 46, 189, 281, 424, 235: 107, 117, 119, 255, 236: 80, 157, 317, 394, 237: 15, 27, 50, 67, 238: 34571, 36746, 42449, 48038, 239: 4, 5, 7, 9, 240: 1722187, 1933783, 2799214, 241: 175, 287, 527, 639, 242: 8, 16, 38, 47, 243: 121, 123, 285, 365, 244: 6, 29, 41, 64, 245: 7, 11, 31, 35, 246: 77, 170, 324, 417, 247: 61, 63, 185, 187, 248: 82, 167, 331, 416, 249: 31, 39, 111, 119, 250: 9788, 23885, 33539, 50450, 251: 5, 7, 8, 13, 252: 45, 116, 144, 208, 253: 255, 327, 507, 691, 254: 4, 11, 16, 19, 255: 245, 365, 493, 499, 256: 38, 194, 467, 524, Code:
b: 1st CK, 2nd CK, 3rd CK, 4th CK 2: 509203, 762701, 777149, 784109, 3: 12119, 20731, 21997, 28297, 4: 361, 919, 1114, 1444, 5: 13, 17, 37, 41, 6: 84687, 133946, 176602, 213410, 7: 457, 1291, 3199, 3313, 8: 14, 112, 116, 148, 9: 41, 49, 74, 121, 10: 334, 1585, 1882, 3340, 11: 5, 7, 17, 19, 12: 376, 742, 1288, 1364, 13: 29, 41, 69, 85, 14: 4, 11, 19, 26, 15: 622403, 1346041, 2742963, 16: 100, 172, 211, 295, 17: 49, 59, 65, 86, 18: 246, 664, 723, 837, 19: 9, 11, 29, 31, 20: 8, 13, 29, 34, 21: 45, 65, 133, 153, 22: 2738, 4461, 6209, 8902, 23: 5, 7, 17, 19, 24: 32336, 69691, 109054, 124031, 25: 105, 129, 211, 313, 26: 149, 334, 1892, 1987, 27: 13, 15, 41, 43, 28: 3769, 9078, 14472, 18211, 29: 4, 9, 11, 13, 30: 4928, 5331, 7968, 8958, 31: 145, 265, 443, 493, 32: 10, 23, 43, 56, 33: 545, 577, 764, 1633, 34: 6, 29, 41, 64, 35: 5, 7, 17, 19, 36: 33791, 79551, 89398, 116364, 37: 29, 77, 113, 163, 38: 13, 14, 25, 53, 39: 9, 11, 29, 31, 40: 25462, 29437, 38539, 52891, 41: 8, 13, 17, 25, 42: 15137, 28594, 45536, 62523, 43: 21, 23, 65, 67, 44: 4, 11, 19, 26, 45: 93, 137, 277, 321, 46: 928, 3754, 4078, 4636, 47: 5, 7, 13, 14, 48: 3226, 4208, 7029, 7965, 49: 81, 129, 229, 241, 50: 16, 35, 67, 86, 51: 25, 27, 77, 79, 52: 25015, 25969, 35299, 60103, 53: 13, 17, 37, 41, 54: 21, 34, 76, 89, 55: 13, 15, 41, 43, 56: 20, 37, 77, 94, 57: 144, 177, 233, 289, 58: 547, 919, 1408, 1957, 59: 4, 5, 7, 9, 60: 20558, 80885, 135175, 202704, 61: 125, 185, 373, 433, 62: 8, 13, 29, 34, 63: 857, 3113, 5559, 6351, 64: 14, 51, 79, 116, 65: 10, 23, 43, 56, 66: 67: 33, 35, 37, 101, 68: 22, 43, 47, 61, 69: 6, 9, 21, 29, 70: 853, 4048, 6176, 15690, 71: 5, 7, 17, 19, 72: 293, 2481, 3722, 4744, 73: 112, 177, 297, 329, 74: 4, 11, 19, 26, 75: 37, 39, 113, 115, 76: 34, 43, 111, 120, 77: 13, 14, 17, 25, 78: 90059, 192208, 294592, 384571, 79: 9, 11, 29, 31, 80: 253, 1037, 6148, 11765, 81: 74, 575, 657, 737, 82: 22326, 36438, 44572, 64905, 83: 5, 7, 8, 13, 84: 16, 69, 101, 154, 85: 173, 257, 517, 601, 86: 28, 59, 115, 146, 87: 21, 23, 65, 67, 88: 571, 862, 898, 961, 89: 4, 11, 17, 19, 90: 27, 64, 118, 155, 91: 45, 47, 137, 139, 92: 32, 61, 125, 154, 93: 189, 281, 565, 612, 94: 39, 56, 134, 151, 95: 5, 7, 17, 19, 96: 38995, 78086, 343864, 540968, 97: 43, 225, 321, 673, 98: 10, 23, 43, 56, 99: 9, 11, 29, 31, 100: 211, 235, 334, 750, 101: 13, 16, 17, 33, 102: 1635, 1793, 4267, 4447, 103: 25, 27, 77, 79, 104: 4, 6, 8, 11, 105: 297, 425, 529, 1273, 106: 13624, 14926, 16822, 19210, 107: 5, 7, 17, 19, 108: 13406, 26270, 43601, 103835, 109: 9, 21, 34, 45, 110: 38, 73, 149, 184, 111: 13, 15, 41, 43, 112: 1357, 3843, 4406, 5084, 113: 20, 37, 49, 65, 114: 24, 91, 139, 206, 115: 57, 59, 173, 175, 116: 14, 25, 53, 64, 117: 149, 221, 237, 353, 118: 50, 69, 169, 188, 119: 4, 5, 7, 9, 120: 121: 100, 163, 211, 232, 122: 14, 40, 83, 112, 123: 13, 61, 63, 154, 124: 92881, 104716, 124009, 170386, 125: 8, 13, 17, 29, 126: 480821, 2767077, 3925190, 127: 2593, 3251, 3353, 6451, 128: 44, 59, 85, 86, 129: 14, 51, 79, 116, 130: 2563, 5896, 11134, 26632, 131: 5, 7, 10, 17, 132: 20, 69, 113, 153, 133: 17, 233, 269, 273, 134: 4, 11, 19, 26, 135: 33, 35, 101, 103, 136: 22195, 47677, 90693, 151660, 137: 17, 22, 25, 47, 138: 1806, 4727, 5283, 6254, 139: 6, 9, 11, 13, 140: 46, 95, 187, 236, 141: 285, 425, 853, 993, 142: 12, 131, 155, 219, 143: 5, 7, 17, 19, 144: 59, 86, 204, 231, 145: 1169, 1313, 3505, 3649, 146: 8, 13, 29, 34, 147: 73, 75, 221, 223, 148: 1936, 5214, 5663, 6557, 149: 4, 9, 11, 13, 150: 49074, 95733, 228764, 539673, 151: 37, 39, 113, 115, 152: 16, 35, 67, 86, 153: 34, 43, 57, 65, 154: 61, 94, 216, 249, 155: 5, 7, 14, 17, 156: 157: 17, 69, 101, 217, 158: 52, 107, 211, 266, 159: 9, 11, 29, 31, 160: 22, 139, 183, 253, 161: 65, 97, 257, 289, 162: 3259, 4726, 9292, 16299, 163: 81, 83, 245, 247, 164: 4, 10, 11, 19, 165: 79, 333, 497, 646, 166: 4174, 9019, 11023, 15532, 167: 5, 7, 8, 13, 168: 4744, 14676, 15393, 20827, 169: 16, 33, 41, 49, 170: 20, 37, 77, 94, 171: 85, 87, 257, 259, 172: 235, 982, 1108, 1171, 173: 13, 17, 28, 37, 174: 6, 21, 29, 41, 175: 21, 23, 65, 67, 176: 58, 119, 235, 296, 177: 209, 268, 577, 1156, 178: 22, 79, 87, 334, 179: 4, 5, 7, 9, 180: 181: 25, 27, 29, 41, 182: 62, 121, 245, 304, 183: 45, 47, 137, 139, 184: 36, 149, 221, 334, 185: 17, 25, 32, 61, 186: 67, 120, 254, 307, 187: 51, 79, 93, 95, 188: 8, 13, 29, 34, 189: 9, 21, 39, 49, 190: 626861, 2121627, 3182252, 3749140, 191: 5, 7, 17, 19, 192: 13897, 19492, 20459, 22968, 193: 484, 5350, 6209, 6401, 194: 4, 11, 14, 19, 195: 13, 15, 41, 43, 196: 1267, 16654, 17920, 20692, 197: 10, 13, 17, 23, 198: 3662, 8425, 10546, 13224, 199: 9, 11, 29, 31, 200: 68, 133, 268, 269, 201: 809, 1009, 2425, 2625, 202: 57, 146, 260, 349, 203: 5, 7, 14, 16, 204: 81, 124, 286, 329, 205: 25, 361, 413, 617, 206: 22, 47, 91, 116, 207: 25, 27, 77, 79, 208: 56, 153, 186, 265, 209: 4, 6, 8, 11, 210: 211: 100, 105, 107, 317, 212: 70, 143, 149, 179, 213: 57, 73, 181, 429, 214: 44, 171, 259, 386, 215: 5, 7, 17, 19, 216: 92, 125, 309, 342, 217: 337, 353, 409, 441, 218: 74, 145, 293, 364, 219: 9, 11, 21, 23, 220: 103, 118, 324, 339, 221: 13, 17, 37, 38, 222: 88530, 90091, 282094, 514016, 223: 13, 15, 41, 43, 224: 4, 11, 19, 26, 225: 3617, 3841, 10849, 11073, 226: 820, 12790, 50257, 53398, 227: 5, 7, 17, 19, 228: 16718, 33891, 35267, 41219, 229: 9, 21, 24, 49, 230: 8, 10, 13, 23, 231: 57, 59, 173, 175, 232: 27760, 72817, 98791, 100576, 233: 14, 17, 25, 53, 234: 46, 189, 281, 424, 235: 64, 117, 119, 172, 236: 80, 157, 317, 394, 237: 29, 33, 41, 50, 238: 17926, 34810, 93628, 99094, 239: 4, 5, 7, 9, 240: 2952972, 2985025, 3695736, 4812046, 241: 65, 177, 417, 529, 242: 14, 73, 101, 116, 243: 121, 123, 365, 367, 244: 6, 29, 41, 64, 245: 13, 17, 37, 40, 246: 77, 170, 324, 417, 247: 61, 63, 185, 187, 248: 82, 167, 331, 416, 249: 41, 49, 121, 129, 250: 9655, 10039, 19828, 23344, 251: 5, 7, 8, 13, 252: 45, 47, 177, 208, 253: 149, 221, 509, 697, 254: 4, 11, 16, 19, 255: 73, 993, 1559, 1639, 256: 100, 172, 211, 295, 

20200619, 17:39  #821 
Nov 2016
5·571 Posts 
the conjectured first 16 Sierpinski/Riesel numbers for bases up to 149 (will complete to bases up to 2048)

20200619, 17:51  #822  
Nov 2016
5·571 Posts 
Quote:
* if k < 44, then there are infinitely many primes of the form (k*128^n+1)/gcd(k+1,1281) with integer n>=1 * if k < 38, then there are infinitely many primes of the form (k*256^n+1)/gcd(k+1,2561) with integer n>=1 * if k < 18, then there are infinitely many primes of the form (k*512^n+1)/gcd(k+1,5121) with integer n>=1 * if k < 81, then there are infinitely many primes of the form (k*1024^n+1)/gcd(k+1,10241) with integer n>=1 * if k < 44, then there are infinitely many primes of the form (k*128^n1)/gcd(k1,1281) with integer n>=1 * if k < 100, then there are infinitely many primes of the form (k*256^n1)/gcd(k1,2561) with integer n>=1 * if k < 14, then there are infinitely many primes of the form (k*512^n1)/gcd(k1,5121) with integer n>=1 * if k < 81, then there are infinitely many primes of the form (k*1024^n1)/gcd(k1,10241) with integer n>=1 

20200619, 17:56  #823  
Nov 2016
5×571 Posts 
Quote:
* For (k*128^n+1)/gcd(k+1,1281), k is not seventh power of integer nor of the form 2^r with integer r == 3 or 5 or 6 mod 7 * For (k*256^n+1)/gcd(k+1,2561), k is not of the form 4*q^4 with integer q * For (k*512^n+1)/gcd(k+1,5121), k is not cube of integer * For (k*1024^n+1)/gcd(k+1,10241), k is not fifth power of integer * For (k*128^n1)/gcd(k1,1281), k is not seventh power of integer * For (k*256^n1)/gcd(k1,2561), k is not square of integer * For (k*512^n1)/gcd(k1,5121), k is not cube of integer * For (k*1024^n1)/gcd(k1,10241), k is not square of integer nor fifth power of integer 

20200619, 18:00  #824  
Nov 2016
5×571 Posts 
Quote:


20200619, 18:06  #825 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
22646_{8} Posts 
what is your reason for quoting huge blocks of text that you posted on the same day?

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