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 Showing results 1 to 25 of 1000 Search took 0.22 seconds. Search: Posts Made By: sweety439
 Forum: sweety439 2021-11-26, 22:14 Replies: 219 Views: 23,018 Posted By sweety439 For families X{Y}Zb = (a*b^n+c)/gcd(a+c,b-1)... For families X{Y}Zb = (a*b^n+c)/gcd(a+c,b-1) (a>=1, b>=2, c != 0, gcd(a,c) = 1, gcd(b,c) = 1), which can be ruled out as only containing composite, which are by covering congruence, and which are by...
 Forum: sweety439 2021-11-26, 17:44 Replies: 219 Views: 23,018 Posted By sweety439 Upload text files, searched up to length 5000 ... Upload text files, searched up to length 5000 For 11{0}1 (the dual of 1{0}11), see https://www.rieselprime.de/ziki/Williams_prime_PP_least For 10{z} (the dual of {z}yz), see...
 Forum: sweety439 2021-11-26, 14:56 Replies: 219 Views: 23,018 Posted By sweety439 e.g. (list all sub-families of given unsolved... e.g. (list all sub-families of given unsolved family, in the same base) base 11 unsolved family 5{7}: {7}: divisible by 7 base 13 unsolved family A{3}A: A{3}: covering set {2,7} {3}A:...
 Forum: sweety439 2021-11-25, 11:48 Replies: 219 Views: 23,018 Posted By sweety439 Now I consider to add these families to the list... Now I consider to add these families to the list (https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml), although...
 Forum: sweety439 2021-11-24, 18:59 Replies: 219 Views: 23,018 Posted By sweety439 Since triangular number * 9 + 1 are always... Since triangular number * 9 + 1 are always triangular numbers, and no triangular numbers > 3 are primes, thus these families in base 9 contain no primes (only count numbers > base), since they can be...
 Forum: sweety439 2021-11-24, 18:45 Replies: 219 Views: 23,018 Posted By sweety439 Our result about minimal primes (start with b+1)... Our result about minimal primes (start with b+1) assume that a number which has passed Millerâ€“Rabin tests (https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test) to the first 9 prime...
 Forum: sweety439 2021-11-24, 18:02 Replies: 163 Views: 22,039 Posted By sweety439 OEIS sequence for Williams primes: 1st:... OEIS sequence for Williams primes: 1st: (b-1)*b^n-1 2nd: (b-1)*b^n+1 3rd: (b+1)*b^n-1 4th: (b+1)*b^n+1 1st dual: b^n-(b-1) 2nd dual: b^n+(b-1) 3rd dual: b^n-(b+1) 4th dual: b^n+(b+1)
 Forum: sweety439 2021-11-23, 18:13 Replies: 219 Views: 23,018 Posted By sweety439 See https://stdkmd.net/nrr/prime/primesize.txt,... See https://stdkmd.net/nrr/prime/primesize.txt, sequences of the form k*10^n+1 includes Generalized Cullen prime numbers, and sequences of the form k*10^n-1 includes Generalized Woodall prime...
 Forum: sweety439 2021-11-23, 15:45 Replies: 219 Views: 23,018 Posted By sweety439 Every base b family is the dual (for the... Every base b family is the dual (for the definition, see http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf and https://oeis.org/A076336/a076336c.html and...
 Forum: sweety439 2021-11-23, 14:29 Replies: 395 Views: 28,381 Posted By sweety439 Since the multiplicative order... Since the multiplicative order (https://en.wikipedia.org/wiki/Multiplicative_order) of b mod prime p (i.e. znorder(Mod(b,p))) always divides p-1, thus, p must divide Phi(n,b) (where Phi is cyclotomic...
 Forum: sweety439 2021-11-21, 15:27 Replies: 219 Views: 23,018 Posted By sweety439 For the forms in... For the forms in https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml, it is conjectured that every base has...
 Forum: sweety439 2021-11-20, 10:57 Replies: 219 Views: 23,018 Posted By sweety439 This problem is better than the original minimal... This problem is better than the original minimal prime problem since this problem is regardless whether 1 is considered as prime or not (https://primes.utm.edu/notes/faq/one.html), i.e. no matter 1...
 Forum: sweety439 2021-11-20, 10:39 Replies: 219 Views: 23,018 Posted By sweety439 Although {z0}z1 almost cannot be minimal prime... Although {z0}z1 almost cannot be minimal prime (start with b+1), but always minimal prime (start with b'+1) in base b'=b^2, its formula is (b^n+1)/(b+1), like the generalized repunit {1} =...
 2021-11-18, 12:30 Replies: 71 Views: 8,410 Posted By sweety439 but A004023 (https://oeis.org/A004023) already... but A004023 (https://oeis.org/A004023) already shown that "8177207" as a(11) ....
 Forum: sweety439 2021-11-18, 12:22 Replies: 395 Views: 28,381 Posted By sweety439 n is a quadratic nonresidue modulo all odd primes... n is a quadratic nonresidue modulo all odd primes p <= sqrt(n) which do not divide n, for these n: {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 27, 30, 32, 33, 35, 38, 42,...
 Forum: sweety439 2021-11-18, 06:09 Replies: 9 Views: 415 Posted By sweety439 Also: Conjecture 1: (A) A143539... Also: Conjecture 1: (A) A143539 (https://oeis.org/A143539) = 0 (AB) A046923 (https://oeis.org/A046923) = 0 (BAA+BBA+CA) A064272 (https://oeis.org/A064272) = 0 (BBA+CA) A002471...
 Forum: sweety439 2021-11-18, 05:41 Replies: 9 Views: 415 Posted By sweety439 The counterexamples listed as sequences: (A)... The counterexamples listed as sequences: (A) Odd counterexamples (AA) Odd prime counterexamples (AB) Odd composite counterexamples (AC) Odd unit (only for "1") counterexamples [note: Odd...
 Forum: sweety439 2021-11-18, 04:56 Replies: 9 Views: 415 Posted By sweety439 For these counterexamples for conjecture 1, all... For these counterexamples for conjecture 1, all numbers >10 except 1542 are == 2 mod 3 (reference: https://oeis.org/A060003, this says that these counterexamples for conjecture 1, all odd numbers >3...
 Forum: sweety439 2021-11-17, 04:20 Replies: 9 Views: 415 Posted By sweety439 PARI/GP program: ... PARI/GP program: isp(n)=(n==0)||(isprime(n)&&n>2) is(n)=for(k=1,n,if(isp((n-2*k^2)/(2-(n%2))),return(0)));1 iss(n)=for(k=1,n,if(isp((n-k*(k+1))/(2-(n%2))),return(0)));1 another PARI/GP...
 Forum: Math 2021-11-17, 03:59 Replies: 0 Views: 75 Posted By sweety439 Conjecture about prime numbers and square/triangular numbers Conjecture 1: Except these 47 numbers, all numbers which is not twice a square number (A001105 (https://oeis.org/A001105)) can be written as (twice a nonzero square number) + (k*p), where k is 1 for...
 Forum: sweety439 2021-11-17, 03:53 Replies: 9 Views: 415 Posted By sweety439 These are: * Numbers not in A001105... These are: * Numbers not in A001105 (https://oeis.org/A001105) which cannot be written as A001105 (https://oeis.org/A001105)(i) + A085118 (https://oeis.org/A085118)(j) for i >= 1, j >= 2 (note:...
 Forum: Math 2021-11-17, 03:00 Replies: 24 Views: 5,610 Posted By sweety439 The largest known pseudoprime (usually,... The largest known pseudoprime (usually, pseudoprime means Fermat pseudoprime to base 2, i.e. A001567 (https://oeis.org/A001567)) is F18233954 (since all composite Fermat number and all composite...
 Forum: sweety439 2021-11-17, 02:51 Replies: 395 Views: 28,381 Posted By sweety439 class number Consider the sequence A061653 (https://oeis.org/A061653)(2*n), since for odd numbers n, the cyclotomic field (https://en.wikipedia.org/wiki/Cyclotomic_field) Q(zeta_n) is the same as that of...
 Forum: sweety439 2021-11-16, 04:00 Replies: 9 Views: 415 Posted By sweety439 Update related text files. Update related text files.
 Forum: sweety439 2021-11-16, 01:34 Replies: 219 Views: 23,018 Posted By sweety439 Using "sub-family", some unsolved families are... Using "sub-family", some unsolved families are obvious through data for minimal primes (start with b+1) base b up to certain limit (https://en.wikiversity.org/wiki/Quasi-minimal_prime): ("proper...
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