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 Showing results 1 to 25 of 1000 Search took 0.26 seconds. Search: Posts Made By: sweety439
 Forum: Miscellaneous Math 2022-06-27, 09:40 Replies: 28 Views: 596 Posted By sweety439 since they are two roots of x^2-x-1, their sum is... since they are two roots of x^2-x-1, their sum is 1 and their product is -1 (in Z/nZ) you can see all modulos < 1000 (https://mersenneforum.org/showpost.php?p=608246&postcount=5) however, for...
 Forum: Miscellaneous Math 2022-06-27, 09:36 Replies: 28 Views: 596 Posted By sweety439 Zp(i) is an quadratic extension field of the... Zp(i) is an quadratic extension field of the field Zp if and only if p == 3 mod 4, if p == 1 mod 4, Zp(i) has zero divisors.
 Forum: sweety439 2022-06-25, 14:20 Replies: 1,270 Views: 104,415 Posted By sweety439 R178 update k=19 has PRP at n=13655 k=4... R178 update k=19 has PRP at n=13655 k=4 remains at n=13K, continuing ....
 Forum: Software 2022-06-24, 14:02 Replies: 5 Views: 197 Posted By sweety439 OK, I will run it myself. OK, I will run it myself.
 Forum: Software 2022-06-24, 13:52 Replies: 5 Views: 197 Posted By sweety439 So can you run the strong Lucas PRP test (with... So can you run the strong Lucas PRP test (with parameters (P, Q) defined by Selfridge's Method A) for these seven numbers?
 Forum: Software 2022-06-24, 13:08 Replies: 5 Views: 197 Posted By sweety439 Can PFGW run the strong Lucas primality test? Can PFGW run the strong Lucas primality test, with parameters (P, Q) defined by Selfridge's Method A (see https://oeis.org/A217255 and http://ntheory.org/pseudoprimes.html)? I have used PFGW to...
 Forum: sweety439 2022-06-24, 06:19 Replies: 351 Views: 44,991 Posted By sweety439 Now these minimal primes (start with b+1) in base... Now these minimal primes (start with b+1) in base b have been proven primes: (only list the numbers > 10^1000) b index of this minimal prime in base b base-b form of the minimal prime algebraic...
 Forum: sweety439 2022-06-24, 06:09 Replies: 351 Views: 44,991 Posted By sweety439 This problem (the minimal prime (start with b+1)... This problem (the minimal prime (start with b+1) problem) covers these problems: * Find the smallest prime of the form (b^n-1)/(b-1) with n>=2 (or prove that such primes do not exist) * Find the...
 Forum: Miscellaneous Math 2022-06-24, 05:57 Replies: 28 Views: 596 Posted By sweety439 You want to use the series 1/0! + 1/1! + 1/2! +... You want to use the series 1/0! + 1/1! + 1/2! + ... to calculated mod 11, but from 1/11!, the denominator is divisible by 11 and you will divide by zero.
 2022-06-24, 05:53 Replies: 164 Views: 36,040 Posted By sweety439 The top Generalized Lucas Number... The top Generalized Lucas Number (https://primes.utm.edu/top20/page.php?id=23) is U(24, - 25, 43201), which is equal to (25^43201+1)/26, but it is still "PRP" in factordb...
 Forum: Factoring 2022-06-22, 14:17 Replies: 500 Views: 76,619 Posted By sweety439 The nontrivial parts are Phi(564,13) and... The nontrivial parts are Phi(564,13) and Phi(576,13), where Phi is the cyclotomic polynomial (https://en.wikipedia.org/wiki/Cyclotomic_polynomial), thus the SNFS difficulty should be...
 Forum: sweety439 2022-06-22, 11:13 Replies: 0 Views: 68 Posted By sweety439 Smallest GFN divisors Smallest k such that k*2^(n+1)+1 is prime and divides GFN(b,n) = b^(2^n)+1 (such prime factors must be == 1 mod 2^(n+1)), for 2<=b<=40, 1<=n<=40 search limit of k: 2^24 b: n = 1 to 40 2: 1,...
 Forum: Factoring 2022-06-22, 08:57 Replies: 500 Views: 76,619 Posted By sweety439 Yes, I copy-and-paste, but copied the wrong... Yes, I copy-and-paste, but copied the wrong texts. So how to use SNFS or GNFS to factor 13^282+1 and 13^288+1? They seems to have low difficulty.
 Forum: Factoring 2022-06-22, 06:53 Replies: 500 Views: 76,619 Posted By sweety439 How to use SNFS or GNFS to factor the composite... How to use SNFS or GNFS to factor the composite cofactors of 13^282+1 and 13^288+1 (they only have 147 digits and 13^288+1, respectively, also their SNFS difficulty are low)
 Forum: sweety439 2022-06-22, 04:14 Replies: 2 Views: 137 Posted By sweety439 Properties of the dozenal system All squares end with square digits (i.e. end with 0, 1, 4 or 9), if n is divisible by both 2 and 3, then n2 ends with 0, if n is not divisible by 2 or 3, then n2 ends with 1, if n is divisible by 2...
 Forum: sweety439 2022-06-22, 03:53 Replies: 2 Views: 137 Posted By sweety439 properties of the number 10 (all written in dozenal) An interesting thing is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + X + E + 10 + ... = −1/10 = −0.1, i.e. $\sum_{k=1}^{\infty}(k)=-\frac{1}{10}=-0.1$ (this number is $\zeta(-1)$ , which equals the...
 Forum: Miscellaneous Math 2022-06-22, 03:45 Replies: 10 Views: 342 Posted By sweety439 Your perfect number is even or odd? All even... Your perfect number is even or odd? All even perfect numbers must be of the form 2^(p-1)*(2^p-1) with 2^p-1 prime.
 Forum: sweety439 2022-06-22, 03:08 Replies: 1,270 Views: 104,415 Posted By sweety439 R165 at n=15K R186 at n=13K R165 at n=15K R186 at n=13K
 Forum: Miscellaneous Math 2022-06-22, 03:04 Replies: 28 Views: 596 Posted By sweety439 I have corrected my program and searched the... I have corrected my program and searched the residues up to mod 1000: 1: 0, 5: 3, 11: 4, 8, 19: 5, 15, 29: 6, 24, 31: 13, 19, 41: 7, 35,
 Forum: Miscellaneous Math 2022-06-21, 11:42 Replies: 28 Views: 596 Posted By sweety439 e and pi are transcendental numbers .... they... e and pi are transcendental numbers .... they cannot be calculated mod n, unless you use 355/113 instead of pi .... the square root of 2 is imaginary number if and only if 2 is not quadratic...
 Forum: Miscellaneous Math 2022-06-21, 11:39 Replies: 28 Views: 596 Posted By sweety439 Phi = (1+sqrt(5))/2, and sqrt(5) mod 11 = 4 or 7... Phi = (1+sqrt(5))/2, and sqrt(5) mod 11 = 4 or 7 (5 has two square roots mod 11: 4 and 7, since 4^2 == 5 mod 11, 7^2 == 5 mod 11), thus Phi == (1+4)/2 == 5/2 == 8 (mod 11) or Phi == (1+7)/2 == 8/2 ==...
 Forum: Lone Mersenne Hunters 2022-06-20, 04:39 Replies: 2,162 Views: 325,319 Posted By sweety439 Your factors are completely wrong. ... Your factors are completely wrong. 509948624278384111727110637486537527543 instead of 50994862427838411172711063748653752754 35645538757884671884030612032344482636735761042071 instead of...
 Forum: Factoring 2022-06-16, 00:02 Replies: 30 Views: 1,828 Posted By sweety439 So can you add 560 to OEIS sequence A242274? So can you add 560 to OEIS sequence A242274?
 Forum: sweety439 2022-06-15, 23:53 Replies: 4 Views: 1,895 Posted By sweety439 I download this... I download this (http://jpenne.free.fr/llr4/cllr401.zip) and run: cllr.exe -q"(57*11^62668-7)/10" But why it cannot work? (For PFGW, I already know how to run)
 Forum: sweety439 2022-06-15, 23:32 Replies: 4 Views: 1,895 Posted By sweety439 I verified that (31^(2^n)+1)/2 is composite for... I verified that (31^(2^n)+1)/2 is composite for n<=23, see...
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