20200614, 10:51  #815  
Nov 2016
13·173 Posts 
Quote:
Corrected: R96 has some k proven composite by partial algebra factors 

20200617, 17:25  #816 
Nov 2016
13×173 Posts 
the conjectured first 4 Sierpinski/Riesel numbers for bases up to 256

20200618, 19:37  #817  
Nov 2016
13·173 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
13×173 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
8C9_{16} 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
13·173 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
13×173 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
13·173 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
13×173 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
4311_{8} Posts 
Quote:


20200619, 18:06  #825 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
79·109 Posts 
what is your reason for quoting huge blocks of text that you posted on the same day?

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Semiprime and nalmost prime candidate for the k's with algebra for the Sierpinski/Riesel problem  sweety439  sweety439  11  20200923 01:42 
The reverse Sierpinski/Riesel problem  sweety439  sweety439  20  20200703 17:22 
The dual Sierpinski/Riesel problem  sweety439  sweety439  12  20171201 21:56 
Sierpinski/ Riesel bases 6 to 18  robert44444uk  Conjectures 'R Us  139  20071217 05:17 
Sierpinski/Riesel Base 10  rogue  Conjectures 'R Us  11  20071217 05:08 