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2 (probable) primes found for R70:
(376*70^6484-1)/3 (496*70^4934-1)/3 k=811 still remains .... |
[URL="https://docs.google.com/document/d/e/2PACX-1vTvi7g8MFqTy_c_u6_k7-0Z5XpSa2ysfNvjltk5Bgvfuw9JULmjkyzs5J3r5fsGC4f1L8Ns5LlL_FA0/pub"]https://docs.google.com/document/d/e/2PACX-1vTvi7g8MFqTy_c_u6_k7-0Z5XpSa2ysfNvjltk5Bgvfuw9JULmjkyzs5J3r5fsGC4f1L8Ns5LlL_FA0/pub[/URL]
Update newest file for Sierpinski problems to include the top 10 (probable) primes for S78, S96, and S126 |
[URL="https://docs.google.com/document/d/e/2PACX-1vQPjYgjFaa0W5koDtgCNeP6y9GerLvxD1L79zfDv4U1-ah4eLG9KWg5yR5nPa3MK3F4yfMpCV9458Wi/pub"]https://docs.google.com/document/d/e/2PACX-1vQPjYgjFaa0W5koDtgCNeP6y9GerLvxD1L79zfDv4U1-ah4eLG9KWg5yR5nPa3MK3F4yfMpCV9458Wi/pub[/URL]
Update newest file for Sierpinski conjectures, according to [URL="http://www.prothsearch.com/fermat.html"]GFN2[/URL] and [URL="http://www.prothsearch.com/GFN10.html"]GFN10[/URL], the test limit of S512 k=2 is (2^54-1)/9-1 = 2001599834386886, and the test limit of S10 k=100 is 2^31-3 = 2147483645 |
[QUOTE=sweety439;555784]S117:
[URL="http://factordb.com/cert.php?id=1100000001094680457"]k=11[/URL] [URL="http://factordb.com/cert.php?id=1100000000936593618"]k=47[/URL] [URL="http://factordb.com/cert.php?id=1100000000936593625"]k=67[/URL] [URL="http://factordb.com/cert.php?id=1100000001094680500"]k=75[/URL] [URL="http://factordb.com/cert.php?id=1100000000936593642"]k=77[/URL] [URL="http://factordb.com/index.php?id=1100000000936593650"]k=81[/URL] (proven by N+1-method) S256: (k=11 is only probable prime) [URL="http://factordb.com/cert.php?id=1100000000001707231"]k=23[/URL] S1024: [URL="http://factordb.com/cert.php?id=1100000000001729238"]k=14[/URL] [URL="http://factordb.com/cert.php?id=1100000000000876912"]k=41[/URL] [URL="http://factordb.com/cert.php?id=1100000000315647263"]k=44[/URL][/QUOTE] R4: [URL="http://factordb.com/cert.php?id=1100000000350048535"]k=106[/URL] R7: (k=197 and 367 are only probable primes) [URL="http://factordb.com/cert.php?id=1100000000854476434"]k=79[/URL] [URL="http://factordb.com/index.php?id=1100000000900876688"]k=139[/URL] (proven by N-1-method) ([URL="http://factordb.com/cert.php?id=1100000000900876693"]certificate for large prime factor for N-1[/URL]) [URL="http://factordb.com/cert.php?id=1100000000887911277"]k=159[/URL] [URL="http://factordb.com/cert.php?id=1100000000900877143"]k=299[/URL] [URL="http://factordb.com/cert.php?id=1100000000887911292"]k=313[/URL] [URL="http://factordb.com/cert.php?id=1100000000887902040"]k=391[/URL] [URL="http://factordb.com/cert.php?id=1100000000887911460"]k=419[/URL] [URL="http://factordb.com/cert.php?id=1100000000887911327"]k=429[/URL] [URL="http://factordb.com/cert.php?id=1100000000900877277"]k=437[/URL] [URL="http://factordb.com/cert.php?id=1100000000900877290"]k=451[/URL] R10: [URL="http://factordb.com/cert.php?id=1100000000291649394"]k=121[/URL] R12: [URL="http://factordb.com/cert.php?id=1100000000800797310"]k=298[/URL] R17: [URL="http://factordb.com/cert.php?id=1100000000033706286"]k=13[/URL] [URL="http://factordb.com/cert.php?id=1100000000889581395"]k=29[/URL] R26: [URL="http://factordb.com/cert.php?id=1100000000894500022"]k=121[/URL] R31: [URL="http://factordb.com/cert.php?id=1100000000900874859"]k=21[/URL] [URL="http://factordb.com/index.php?id=1100000000900875104"]k=39[/URL] (proven by N-1-method) ([URL="http://factordb.com/cert.php?id=1100000000900875163"]certificate for large prime factor for N-1[/URL]) [URL="http://factordb.com/cert.php?id=1100000000903614099"]k=49[/URL] [URL="http://factordb.com/cert.php?id=1100000000903614151"]k=113[/URL] [URL="http://factordb.com/cert.php?id=1100000000900875383"]k=115[/URL] [URL="http://factordb.com/cert.php?id=1100000000903614183"]k=123[/URL] [URL="http://factordb.com/cert.php?id=1100000000903614239"]k=124[/URL] R33: [URL="http://factordb.com/cert.php?id=1100000000929860528"]k=213[/URL] R35: [URL="http://factordb.com/index.php?id=1100000000012776520"]k=1[/URL] (proven by N-1-method) R37: [URL="http://factordb.com/index.php?id=1100000000916996761"]k=5[/URL] (proven by N-1-method) R39: [URL="http://factordb.com/index.php?id=1100000000012789513"]k=1[/URL] (proven by N-1-method) R43: [URL="http://factordb.com/index.php?id=1100000000904478431"]k=4[/URL] (proven by N-1-method) R45: [URL="http://factordb.com/cert.php?id=1100000000920998225"]k=53[/URL] |
5 Attachment(s)
[QUOTE=sweety439;555375]Update files.[/QUOTE]
Update files |
Also reserved R88 and found these (probable) primes:
(49*88^2223-1)/3 (79*88^7665-1)/3 (235*88^1330-1)/3 (346*88^2969-1)/3 (541*88^1187-1)/3 (544*88^8904-1)/3 k = 46, 94, 277, 508 are still remaining. |
Still no (probable) prime found for R70 k=811
If a (probable) prime for R70 k=811 were found, then will produce a group of 11 consecutive proven Riesel conjectures: R67 to R77 |
[QUOTE=sweety439;556068]R4:
[URL="http://factordb.com/cert.php?id=1100000000350048535"]k=106[/URL] R7: (k=197 and 367 are only probable primes) [URL="http://factordb.com/cert.php?id=1100000000854476434"]k=79[/URL] [URL="http://factordb.com/index.php?id=1100000000900876688"]k=139[/URL] (proven by N-1-method) ([URL="http://factordb.com/cert.php?id=1100000000900876693"]certificate for large prime factor for N-1[/URL]) [URL="http://factordb.com/cert.php?id=1100000000887911277"]k=159[/URL] [URL="http://factordb.com/cert.php?id=1100000000900877143"]k=299[/URL] [URL="http://factordb.com/cert.php?id=1100000000887911292"]k=313[/URL] [URL="http://factordb.com/cert.php?id=1100000000887902040"]k=391[/URL] [URL="http://factordb.com/cert.php?id=1100000000887911460"]k=419[/URL] [URL="http://factordb.com/cert.php?id=1100000000887911327"]k=429[/URL] [URL="http://factordb.com/cert.php?id=1100000000900877277"]k=437[/URL] [URL="http://factordb.com/cert.php?id=1100000000900877290"]k=451[/URL] R10: [URL="http://factordb.com/cert.php?id=1100000000291649394"]k=121[/URL] R12: [URL="http://factordb.com/cert.php?id=1100000000800797310"]k=298[/URL] R17: [URL="http://factordb.com/cert.php?id=1100000000033706286"]k=13[/URL] [URL="http://factordb.com/cert.php?id=1100000000889581395"]k=29[/URL] R26: [URL="http://factordb.com/cert.php?id=1100000000894500022"]k=121[/URL] R31: [URL="http://factordb.com/cert.php?id=1100000000900874859"]k=21[/URL] [URL="http://factordb.com/index.php?id=1100000000900875104"]k=39[/URL] (proven by N-1-method) ([URL="http://factordb.com/cert.php?id=1100000000900875163"]certificate for large prime factor for N-1[/URL]) [URL="http://factordb.com/cert.php?id=1100000000903614099"]k=49[/URL] [URL="http://factordb.com/cert.php?id=1100000000903614151"]k=113[/URL] [URL="http://factordb.com/cert.php?id=1100000000900875383"]k=115[/URL] [URL="http://factordb.com/cert.php?id=1100000000903614183"]k=123[/URL] [URL="http://factordb.com/cert.php?id=1100000000903614239"]k=124[/URL] R33: [URL="http://factordb.com/cert.php?id=1100000000929860528"]k=213[/URL] R35: [URL="http://factordb.com/index.php?id=1100000000012776520"]k=1[/URL] (proven by N-1-method) R37: [URL="http://factordb.com/index.php?id=1100000000916996761"]k=5[/URL] (proven by N-1-method) R39: [URL="http://factordb.com/index.php?id=1100000000012789513"]k=1[/URL] (proven by N-1-method) R43: [URL="http://factordb.com/index.php?id=1100000000904478431"]k=4[/URL] (proven by N-1-method) R45: [URL="http://factordb.com/cert.php?id=1100000000920998225"]k=53[/URL][/QUOTE] R46: (k=86, 576, and 561 are only probable primes) [URL="http://factordb.com/cert.php?id=1100000001506871168"]k=100[/URL] [URL="http://factordb.com/cert.php?id=1100000000929848973"]k=121[/URL] [URL="http://factordb.com/cert.php?id=1100000000929850622"]k=142[/URL] [URL="http://factordb.com/cert.php?id=1100000000929849002"]k=256[/URL] [URL="http://factordb.com/cert.php?id=1100000001506870486"]k=386[/URL] R49: [URL="http://factordb.com/cert.php?id=1100000000854476434"]k=79[/URL] R51: [URL="http://factordb.com/cert.php?id=1100000000467236538"]k=1[/URL] R57: [URL="http://factordb.com/index.php?id=1100000000920998155"]k=87[/URL] (proven by N-1-method) ([URL="http://factordb.com/cert.php?id=1100000000920998157"]certificate for large prime factor for N-1[/URL]) R58: (k=382, 400, and 421 are only probable primes) [URL="http://factordb.com/index.php?id=1100000000904478808"]k=4[/URL] (proven by N-1-method) [URL="http://factordb.com/cert.php?id=1100000000920998300"]k=103[/URL] [URL="http://factordb.com/cert.php?id=1100000000920998307"]k=109[/URL] [URL="http://factordb.com/cert.php?id=1100000000929858329"]k=142[/URL] [URL="http://factordb.com/cert.php?id=1100000000929858373"]k=163[/URL] [URL="http://factordb.com/cert.php?id=1100000000929858343"]k=217[/URL] [URL="http://factordb.com/cert.php?id=1100000001571684713"]k=271[/URL] [URL="http://factordb.com/cert.php?id=1100000000929853580"]k=334[/URL] [URL="http://factordb.com/cert.php?id=1100000001571684796"]k=361[/URL] [URL="http://factordb.com/cert.php?id=1100000001571684841"]k=379[/URL] [URL="http://factordb.com/cert.php?id=1100000000929856391"]k=445[/URL] [URL="http://factordb.com/cert.php?id=1100000000929855094"]k=457[/URL] [URL="http://factordb.com/cert.php?id=1100000001506867848"]k=487[/URL] R61: (k=13 is only probable prime) [URL="http://factordb.com/cert.php?id=1100000000920955907"]k=10[/URL] [URL="http://factordb.com/cert.php?id=1100000000920994856"]k=41[/URL] [URL="http://factordb.com/cert.php?id=1100000000920985589"]k=77[/URL] |
Update newest file for [URL="https://docs.google.com/document/d/e/2PACX-1vQNF_fb-CvXwTM-kpioItuyJQyfPSPCka3CRcHWUGHsux-Yi3l9O6gCdQTxLfccG6qVO6E5UYhW6niC/pub"]Riesel problems[/URL] to include recent status for R70 and R88
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I conjectured that:
If (k,b,c) is integer triple, k>=1, b>=2, c != 0, gcd(k,c)=1, gcd(b,c)=1, if (k*b^n+c)/gcd(k+c,b-1) does not have covering set of primes for the n such that: (the set of the n satisfying these conditions must be nonempty, or (k*b^n+c)/gcd(k+c,b-1) proven composite by full algebra factors) * if c != +-1, (let r be the largest integer such that (-c) is perfect r-th power) k*b^n is not perfect r-th power * if c = 1, k*b^n is not perfect odd power (of the form m^r with odd r>1), except the case: b = q^m, k = q^r, where q is not of the form t^s with odd s>1, and m and r have no common odd prime factor, and the exponent of highest power of 2 dividing r < the exponent of highest power of 2 dividing m * if c = -1, k*b^n is not perfect power (of the form m^r with r>1), except the case: b = q^m, k = q^r, where q is not of the form t^s with odd s>1, and m and r have no common odd prime factor * 4*k*b^n*c is not perfect 4-th power Then there are infinitely many primes of the form (k*b^n+c)/gcd(k+c,b-1), except the case: b = q^m, k = q^r, where q is not of the form t^s with odd s>1, and m and r have no common odd prime factor, and the exponent of highest power of 2 dividing r >= the exponent of highest power of 2 dividing m, and the equation 2^x = r (mod m) has no solution. |
[QUOTE=sweety439;550364]Also these cases:
S15 k=343: since 343 is cube, all n divisible by 3 have algebra factors, and we only want to know whether it has a covering set of primes for all n not divisible by 3, if so, then this k makes a full covering set with algebraic factors and be excluded from the conjecture; if not, then this k does not make a full covering set with algebraic factors and be included from the conjecture. n-value : factors 1 : 31 · 83 2 : 2^2 · 11 · 877 4 : 2^2 · 809 · 2683 5 : 811 · 160583 7 : 11^2 · 242168453 11 : 31 · 101 · 25357 · 18684739 13 : 397 · 1281101 · 656261029 17 : 11 · 27479311 · 55900668804553 29 : 53 · 197741 · 209188613429183386499227445981 35 : 1337724923 · 18667724069720862256321575167267431 43 : 20943991 · 3055827403675875709696160949928034201885723243 61 : 23539 · (a 61-digit prime) and it does not appear to be any covering set of primes, so there must be a prime at some point. S61 k=324: since 324 is of the form 4*m^4, all n divisible by 4 have algebra factors, and we only want to know whether it has a covering set of primes for all n not divisible by 4, if so, then this k makes a full covering set with algebraic factors and be excluded from the conjecture; if not, then this k does not make a full covering set with algebraic factors and be included from the conjecture. n-value : factors 1 : 59 · 67 2 : 41 · 5881 3 : 13 · 1131413 5 : 5 · 7 · 1563709723 6 : 13 · 256809250661 7 : 23 · 1255679 · 7051433 13 : 191 · 7860337 · 27268229 · 256289843 14 : 1540873 · 1698953 · 244480646906833 31 : 1888149043321 · 441337391577139 · 1721840403480692512106884569347 34 : 10601 · 174221 · (a 54-digit prime) and it does not appear to be any covering set of primes, so there must be a prime at some point.[/QUOTE] The case for R40 k=490, since all odd n have algebra factors, we only consider even n: n-value : factors 2 : 3^3 · 9679 4 : 43 · 79 · 83 · 1483 6 : 881 · 759379493 8 : 3 · 356807111111111 10 : 31 · 67883 · 813864335521 12 : 53 · 51703370062893081761 18 : 163 · 68860007363271983640081799591 22 : 4801 · 23279 · 3561827 · 4036715519 · 17881240410679 28 : 210323 · 6302441 · 88788971627962097615055082730651231 30 : 38270136643 · 4920560231486977484668641122451121981831 and it does not appear to be any covering set of primes, so there must be a prime at some point. R40 also has two special remain k: 520 and 11560, 520 = 13 * base, 11560 = 289 * base, and the further searching for k = 11560 is k = 289 with odd n > 1 (since 289 is square, all even n for k = 289 have algebra factors) Another base is R106, which has many k with algebra factors (these k are all squares): 64 = 2^6 (thus, all n == 0 mod 2 and all n == 0 mod 3 have algebra factors) 81 = 3^4 (thus, all n == 0 mod 2 have algebra factors) 400 = 20^2 (thus, all n == 0 mod 2 have algebra factors) 676 = 26^2 (thus, all n == 0 mod 2 have algebra factors) 841 = 29^2 (thus, all n == 0 mod 2 have algebra factors) 1024 = 2^10 (thus, all n == 0 mod 2 and all n == 0 mod 5 have algebra factors) We should check whether they have covering set for the n which do not have algebra factors, like the case for R30 k=1369 and R88 k=400 |
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