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 Showing results 1 to 25 of 1000 Search took 0.22 seconds. Search: Posts Made By: sweety439
 Forum: sweety439 2021-12-07, 14:15 Replies: 227 Views: 24,117 Posted By sweety439 For GFN families in bases b <= 1024 which are odd... For GFN families in bases b <= 1024 which are odd powers (i.e. in https://oeis.org/A070265) (other bases already have information in http://jeppesn.dk/generalized-fermat.html and...
 Forum: sweety439 2021-12-06, 10:14 Replies: 227 Views: 24,117 Posted By sweety439 Forms in... Forms in https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml: 1{0}2 b^n+2:...
 Forum: sweety439 2021-11-30, 20:52 Replies: 227 Views: 24,117 Posted By sweety439 Update data for minimal primes, see... Update data for minimal primes, see https://sites.google.com/view/data-of-minimal-primes
 Forum: sweety439 2021-11-30, 20:41 Replies: 227 Views: 24,117 Posted By sweety439 In base 10, a sting is primefree string if and... In base 10, a sting is primefree string if and only if: The string is of the form {0}S{0,2,4,5,6,8} and S is of one of these forms: * empty string * "gcd of its digits" <> 1 (note: gcd(0,n) =...
 Forum: sweety439 2021-11-30, 19:59 Replies: 227 Views: 24,117 Posted By sweety439 more datas more datas
 Forum: sweety439 2021-11-28, 19:42 Replies: 136 Views: 19,629 Posted By sweety439 For the minimal set of "noncomposites" (i.e. 0,... For the minimal set of "noncomposites" (i.e. 0, 1, primes), all bases <=24 are completely solved: b largest minimal noncomposite 2 1 3 2 4 3 5 3 6 5 7 5
 Forum: sweety439 2021-11-28, 17:23 Replies: 227 Views: 24,117 Posted By sweety439 This is the text file for {z0}z1 (i.e.... This is the text file for {z0}z1 (i.e. generalized Wagstaff primes, see A084742 (https://oeis.org/A084742), but exclude p=3, and use the length of the primes (i.e. use p-1 instead of p)), also...
 Forum: sweety439 2021-11-28, 17:20 Replies: 227 Views: 24,117 Posted By sweety439 These are all minimal primes (start with b+1) in... These are all minimal primes (start with b+1) in base b=25 up to 2^32 Base 25 is a very hard base (however, of course, bases > 25 which are coprime to 6 are harder than it), we can imagine an...
 Forum: sweety439 2021-11-28, 15:12 Replies: 136 Views: 19,629 Posted By sweety439 If 1 is regarded as prime... If 1 is regarded as prime (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.pdf), then all bases <=20 are solved, in fact, all bases <=24 except the base 21 family G{0}FK is solved. b ...
 Forum: sweety439 2021-11-26, 22:14 Replies: 227 Views: 24,117 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 22,225 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 28,668 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 227 Views: 24,117 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: 8,722 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: 28,668 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: 502 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...
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