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 Showing results 1 to 25 of 1000 Search took 0.27 seconds. Search: Posts Made By: sweety439
 Forum: Homework Help 2022-06-29, 18:11 Replies: 6 Views: 377 Posted By sweety439 7 and 13 are unique primes in base 2 7 is... 7 and 13 are unique primes in base 2 7 is the only prime with period length 3 in base 2, and 13 is the only prime with period length 12 in base 2 see factorization of Phi(n,2)...
 Forum: sweety439 2022-06-29, 10:04 Replies: 43 Views: 7,181 Posted By sweety439 pdf file for broken link... pdf file for broken link https://cbright.myweb.cs.uwindsor.ca/reports/cs662-problem12.pdf from wayback machine:...
 Forum: sweety439 2022-06-29, 10:03 Replies: 43 Views: 7,181 Posted By sweety439 pdf files related to minimal primes: Link 1:... pdf files related to minimal primes: Link 1: https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf Link 2: https://cs.uwaterloo.ca/~shallit/Papers/br10.pdf Link 3:...
 Forum: sweety439 2022-06-29, 10:00 Replies: 43 Views: 7,181 Posted By sweety439 Local copies of the pdf files: Original... Local copies of the pdf files: Original links of these pdf files: Link 1: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf Link 2:...
 Forum: Factoring 2022-06-28, 17:32 Replies: 502 Views: 76,848 Posted By sweety439 What is the approximately equivalent for SNFS and... What is the approximately equivalent for SNFS and GNFS? I guess that SNFS difficulty n is approximately equivalent to GNFS difficulty (2/3)*n, however, if my guess is true, then SNFS 210 is...
 Forum: Miscellaneous Math 2022-06-27, 09:40 Replies: 28 Views: 648 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: 648 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: 104,534 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: 203 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: 203 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: 203 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: 45,105 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: 45,105 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: 648 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: 36,091 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: 502 Views: 76,848 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: 74 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: 502 Views: 76,848 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: 502 Views: 76,848 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: 143 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: 143 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: 344 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: 104,534 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: 648 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: 648 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...
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