2018-02-26, 18:18 | #12 |
Feb 2018
2^{5}×3 Posts |
some "must be" M() values:
( 3: 2) ( 5: 4) ( 7: 3) ( 9: 6)(11:10) (13:12) (15: 4) (17: 8) (19:18)(21: 6) (23:11) (25:20) (27:18) (29:28) not? |
2018-02-27, 04:09 | #13 |
Romulan Interpreter
Jun 2011
Thailand
3×2,957 Posts |
three observations:
1. the expression "a*b/gcd(a,b)" is usually called "lcm(a,b)", simpler to write... 2. in each of your pairs (x,y) the y is the order of 2 (mod x). In pari/gp, you can get it with the function "znorder". Not more than few days ago, we posted a function in a parallel thread, that computes the same thing, it is called "getp()", look for it.... (it also works for all odd numbers, not necessarily prime). Code:
gp > znorder(Mod(2,3)) = 2 gp > znorder(Mod(2,5)) = 4 gp > znorder(Mod(2,7)) = 3 gp > znorder(Mod(2,9)) = 6 gp > getp(9) = 6 gp > getp(25) = 20 gp > Last fiddled with by LaurV on 2018-02-27 at 04:21 |
2018-02-27, 09:52 | #14 |
Feb 2018
2^{5}·3 Posts |
oh, functions, thanks
wieferich ... wait ... ¿ Conjecture ? ¿ what conjecture ? |
2018-02-27, 11:50 | #15 |
Feb 2018
2^{5}·3 Posts |
M( 1093 ) = 364
M( 3511 ) = 1755 |
2018-02-27, 15:36 | #16 |
Feb 2017
Nowhere
110111111000_{2} Posts |
Even with your conditions in post #8 and post #11 to this thread [M(p) divides p-1, and if p = 2^e - 1 then M(p) = e], your "function" is only defined unambiguously if either
(1) p is a Mersenne prime, or (2) 2 is a primitive root (mod p). Up to the limit 200, the following primes do not satisfy either condition: For p = 17, the possible values of M(p) are 8 times k for k in [1, 2]. For p = 23, the possible values of M(p) are 11 times k for k in [1, 2]. For p = 41, the possible values of M(p) are 20 times k for k in [1, 2]. For p = 43, the possible values of M(p) are 14 times k for k in [1, 3]. For p = 47, the possible values of M(p) are 23 times k for k in [1, 2]. For p = 71, the possible values of M(p) are 35 times k for k in [1, 2]. For p = 73, the possible values of M(p) are 9 times k for k in [1, 2, 4, 8]. For p = 79, the possible values of M(p) are 39 times k for k in [1, 2]. For p = 89, the possible values of M(p) are 11 times k for k in [1, 2, 4, 8]. For p = 97, the possible values of M(p) are 48 times k for k in [1, 2]. For p = 103, the possible values of M(p) are 51 times k for k in [1, 2]. For p = 109, the possible values of M(p) are 36 times k for k in [1, 3]. For p = 113, the possible values of M(p) are 28 times k for k in [1, 2, 4]. For p = 137, the possible values of M(p) are 68 times k for k in [1, 2]. For p = 151, the possible values of M(p) are 15 times k for k in [1, 2, 5, 10]. For p = 157, the possible values of M(p) are 52 times k for k in [1, 3]. For p = 167, the possible values of M(p) are 83 times k for k in [1, 2]. For p = 191, the possible values of M(p) are 95 times k for k in [1, 2]. For p = 193, the possible values of M(p) are 96 times k for k in [1, 2]. For p = 199, the possible values of M(p) are 99 times k for k in [1, 2]. If you want M(p) to be the multiplicative order of 2 (mod p), please just say so. |
2018-02-27, 15:45 | #17 |
Feb 2018
2^{5}×3 Posts |
I think the function M() is what user "a3call" names "reverse factoring".
Next post , the method i use on my theories to get M(n). But i suspect the method used for a3call is much better. Sorry ¿ some place to share a windows64.exe ? JM M (If times count, of course. Im waiting for one cheap q-computer) |
2018-02-27, 15:47 | #18 |
Feb 2018
2^{5}·3 Posts |
relating m order of 2 mod p:
Any idea of what it means. :-) JM M |
2018-02-27, 15:55 | #19 |
Feb 2018
2^{5}·3 Posts |
pseudocode tserie
init vars: M=0, e=eStart, D=1, PD=1. begin loop Use the step equation to get g, e' M =M+g PD =PD*(2^g) Si (e')!=(eEnd), D=D+PD e =e' Exit loop when "e=eEnd"; loopend return values M,D. end For the M() function, the step eq. is n+e = (2^g)*(e') eStart=1 eEnd=1 |
2018-02-27, 16:20 | #20 |
Feb 2018
2^{5}·3 Posts |
Someone asked to "a1call" values of 64 bits for their rev-fact.
Well here someones of 30b, now. M M 52667 n 1073814919 Nbit 10 D 0 Dbit 26123 Mi 52667 M M 5711 n 1073814943 Nbit 12 D 0 Dbit 2851 Mi 5711 M M 18979 n 1073815079 Nbit 10 D 0 Dbit 9526 Mi 18979 w M 22 n 1073815151 Nbit 12 D 2097009 Dbit 17 Mi 11 M M 14639 n 1073815187 Nbit 10 D 0 Dbit 7234 Mi 14639 w M 13474 n 1073815447 Nbit 12 D 0 Dbit 6700 Mi 6737 w M 2066 n 1073815507 Nbit 12 D 0 Dbit 1021 Mi 1033 w M 18982 n 1073815531 Nbit 13 D 0 Dbit 9476 Mi 9491 M M 52553 n 1073815759 Nbit 9 D 0 Dbit 26315 Mi 52553 w M 13274 n 1073815933 Nbit 10 D 0 Dbit 6747 Mi 6637 Explain: n, M(n). n*D = 2^M-1 Si D is unknow, we know the number of bits ONE of D. Mi : part odd of M. That is for Wagstaff numbers. |
2018-03-01, 11:03 | #21 |
Feb 2018
2^{5}×3 Posts |
A windows exe to find values of M() function.
Hi,
One free tool. JM M Last fiddled with by Batalov on 2018-03-01 at 15:45 Reason: blind executable attachment is removed |
2018-03-01, 15:44 | #22 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 Posts |
You can only attach the executables after you have demonstrated the source.
We don't need potential malware on this site. Attachment deleted. |
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