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 2018-02-26, 18:18 #12 JM Montolio A   Feb 2018 9610 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 LaurV Romulan Interpreter     Jun 2011 Thailand 22·7·11·29 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 > 3. we see where you are going with this, but it will not work. Sooner or later you will run into an obstacle called "wieferich primes" and you will not be able to progress any further. The most of the guys in the world trying to prove this conjecture failed because they never heard of wieferich primes before... Last fiddled with by LaurV on 2018-02-27 at 04:21
 2018-02-27, 09:52 #14 JM Montolio A   Feb 2018 25·3 Posts oh, functions, thanks wieferich ... wait ... ¿ Conjecture ? ¿ what conjecture ?
 2018-02-27, 11:50 #15 JM Montolio A   Feb 2018 25·3 Posts M( 1093 ) = 364 M( 3511 ) = 1755
 2018-02-27, 15:36 #16 Dr Sardonicus     Feb 2017 Nowhere EE916 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 JM Montolio A   Feb 2018 6016 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 JM Montolio A   Feb 2018 25×3 Posts relating m order of 2 mod p: Any idea of what it means. :-) JM M
 2018-02-27, 15:55 #19 JM Montolio A   Feb 2018 9610 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 JM Montolio A   Feb 2018 25·3 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 JM Montolio A   Feb 2018 25·3 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 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,161 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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