20200721, 03:28  #23  
Nov 2016
23×97 Posts 
Quote:


20200721, 03:40  #24  
May 2007
Kansas; USA
2^{3}×3×5^{2}×17 Posts 
Quote:
We simply need this error check removed from srsieve and/or srsieve2. Last fiddled with by gd_barnes on 20200721 at 03:41 

20200721, 03:49  #25  
Nov 2016
23×97 Posts 
Quote:


20200721, 07:41  #26  
Mar 2006
Germany
101100011101_{2} Posts 
Quote:
Code:
ERROR: Sieve range P0 <= p <= P1 must be in 43 < P0 < P1 < 2^62. 

20200721, 15:01  #27 
Nov 2016
23·97 Posts 
okay, I used srsieve for R36, sieved k*36^n1 start with p=11 (to p=10^8) for these 193 k's (which remain at n=1000): {251, 260, 924, 1148, 1356, 1555, 1923, 2110, 2133, 2443, 2753, 2776, 3181, 3590, 3699, 3826, 3942, 4241, 4330, 4551, 4635, 4737, 4865, 5027, 5196, 5339, 5483, 5581, 5615, 5791, 5853, 6069, 6236, 6542, 6581, 6873, 6883, 7101, 7253, 7316, 7362, 7399, 7445, 7617, 7631, 7991, 8250, 8259, 8321, 8361, 8363, 8472, 8696, 9140, 9156, 9201, 9469, 9491, 9582, 10695, 10913, 11010, 11014, 11143, 11212, 11216, 11434, 11568, 11904, 12174, 12320, 12653, 12731, 12766, 13641, 13800, 14191, 14358, 14503, 14540, 14799, 14836, 14973, 14974, 15228, 15578, 15656, 15687, 15756, 15909, 16168, 16908, 17013, 17107, 17354, 17502, 17648, 17749, 17881, 17946, 18203, 18342, 18945, 19035, 19315, 19389, 19572, 19646, 19907, 20092, 20186, 20279, 20485, 20630, 20684, 21162, 21415, 21880, 22164, 22312, 22793, 23013, 23126, 23182, 23213, 23441, 23482, 23607, 23621, 23792, 23901, 23906, 23975, 24125, 24236, 24382, 24556, 24645, 24731, 24887, 24971, 25011, 25052, 25159, 25161, 25204, 25679, 25788, 25831, 26107, 26160, 26355, 26382, 26530, 26900, 27161, 27262, 27296, 27342, 27680, 27901, 28416, 28846, 28897, 29199, 29266, 29453, 29741, 29748, 29847, 30031, 30161, 30970, 31005, 31190, 31326, 31414, 31634, 31673, 31955, 32154, 32302, 32380, 32411, 32451, 32522, 32668, 32811, 33047, 33516, 33627, 33686, 33762} and for 1001<=n<=10^5, then changed the first row of the t17_b36 file to "ABC ($a*36^$b1)/gcd($a1,35)", then used pfgw to test the primality of these numbers.

20200721, 15:17  #28 
Nov 2016
100010110111_{2} Posts 
currently R36 (with CK=33791) at n=10K, with these k's remain: {1148, 1555, 2110, 2133, 3699, 4551, 4737, 6236, 6883, 7253, 7362, 7399, 7991, 8250, 8361, 8363, 8472, 9491, 9582, 11014, 12320, 12653, 13641, 14358, 14540, 14836, 14973, 14974, 15228, 15687, 15756, 15909, 16168, 17354, 17502, 17946, 18203, 19035, 19646, 20092, 20186, 20630, 21880, 22164, 22312, 23213, 23901, 23906, 24236, 24382, 24645, 24731, 24887, 25011, 25159, 25161, 25204, 25679, 25788, 26160, 26355, 27161, 29453, 29847, 30970, 31005, 31634, 32302, 33047, 33627}, I know that square k's proven composite by full algebra factors (except k=1, since for n=2, (1*36^21)/gcd(11,361) = 37 is prime, however k=1 can only have this prime and cannot have no more primes (thus cannot have infinitely many primes), thus k=1 is still excluded from the conjecture (see post https://mersenneforum.org/showpost.p...&postcount=315 for more information), a kvalue is included from the conjecture if and only if this kvalue may have infinitely many primes; also, I know that the k's such that gcd(k1,361) = 1 is completely the same as the R36 problem in CRUS for these k's, however I don't have the primes for these k's other than the top 10 primes in CRUS (since gcd(337911,361) is not 1, thus the CK for the CRUS R36 conjecture cannot be 33791 (it is 116364)), thus I only listed the (probable) primes for n<=10K (in which I have searched) in the file, the (probable) primes for 1K<n<=10K are in post https://mersenneforum.org/showpost.p...&postcount=779

20200725, 20:16  #29 
Nov 2016
23·97 Posts 
Found the conjectured smallest Sierpinski/Riesel numbers for bases <= 2500
* Only the k's with covering set are considered as Sierpinski/Riesel numbers, kvalues that make a full covering set with all or partial algebraic factors are excluded from the conjectures. * Searched to k=5M, listed "NA" if the conjectured smallest Sierpinski/Riesel number for this base is >5M (i.e. there is no k <= 5M with covering set) * Test limit: primes in the covering set <= 100K, exponents <= 2100 
20200917, 16:55  #30 
Nov 2016
23×97 Posts 
The mixed Sierpinski/Riesel conjectures for prime bases
This project is from the article http://www.kurims.kyotou.ac.jp/EMIS...rs/i61/i61.pdf, this article is about the mixed Sierpinski (base 2) theorem, which is that for every odd k<78557, there is a prime either of the form k*2^n+1 or of the form 2^n+k, we generalized this theorem (may be only conjectures to other bases) to other prime bases (since the dual form for composite bases is more complex when gcd(k,b) > 1 (see thread https://mersenneforum.org/showthread.php?t=21954), we only consider prime bases), we conjectured that for every k<the CK for the Sierpinski conjecture base b (for prime b) which is not divisible by b, there is a prime either of the form k*b^n+1 or of the form b^n+k
We can also generalize this problem to the Riesel side, for the classic (base 2) mixed Riesel problem, there is only 7 unsolved kvalues: 2293, 196597, 304207, 342847, 344759, 386801, 444637 (and plus this 2 kvalues if probable primes cannot be consider as primes: 363343 and 384539) (see thread https://mersenneforum.org/showthread.php?t=6545), we conjectured that for every k<the CK for the Riesel conjecture base b (for prime b) which is not divisible by b, there is a prime either of the form k*b^n1 or of the form b^nk Note that the weight of b^n+k is the same as that of k*b^n+1, and the weight of b^nk is the same as that of k*b^n1, if gcd(k,b)=1 S3 and S7 have too many k's remain, for S5, we have these primes: Code:
5^24+6436 5^36+7528 5^144+10918 5^1505+26798 5^4+29914 5^458+36412 5^3+41738 5^9+44348 5^485+44738 5^12+45748 5^12+51208 5^46+58642 5^12+60394 5^2+62698 5^2+64258 5^10+67612 5^41+67748 5^13+71492 5^74+74632 5^7+76724 5^3+83936 5^21+84284 5^181+90056 5^23+92906 5^4+93484 5^11+105464 5^11+126134 5^1+139196 5^15+152588 S11 and S13 are already proven, for S17, 17^838+244 is prime, thus, the mixed Sierpinski conjecture base 17 is also a theorem. For the Riesel side, R3 and R7 also have too many k remain, for R5, we have these primes: Code:
5^13622 5^114906 5^92023906 5^626222 5^19935248 5^1252922 5^963838 5^664598 5^69571146 5^3576354 5^24109862 5^65127174 5^27131848 ... R11, R13, and R17 are already proven. Last fiddled with by sweety439 on 20200917 at 17:21 
20200917, 17:12  #31 
Nov 2016
100010110111_{2} Posts 
Also, 31^555758 is prime, thus the mixed Riesel conjecture base 31 is also a theorem.
For the S37 case, 37^1+94, 37^5+1272, and 37^2+2224 are primes, thus the mixed Sierpinski conjecture base 37 is also a theorem. For the S43 case, 43^n+166 is composite for all small n, thus the mixed Sierpinski conjecture base 43 is still unsolved. For the R23 case, 23^568404 is prime, thus the mixed Riesel conjecture base 23 is also a theorem. R37 case has 3 kvalues remain: 1578, 6752, and 7352: Code:
37^3522 37^30816 37^41614 37^12148 37^2982640 37^33972 37^14428 37^4015910 37^337088 
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