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Old 2017-12-28, 13:29   #40
Romulan Interpreter
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"name field"
Jun 2011

34·112 Posts

Originally Posted by gophne View Post
I will consider to leave this site voluntarily and won't post anything again under any name.
Now, that is not necessary! We all make mistakes, and as other people here said, recognizing when we make mistakes and willing to learn from it is a big quality of a person. We wish you to stay, and continue to play with numbers, maybe read some more theory, and in the future you may really find something worthy.

About that "quality of a person" for example, (hehe) I was one order of magnitude off with the estimation of the time that one will need to test all mersenne numbers with a prime exponent up to e(M34) with LL test, in pari. One will need not 3-4 days, but maybe 30-40 days, with a 4 core computer. The tests in the 1.2 millions take close to one hour each... (this was not really a miscalculation, but mostly trying to lay a trap for you, hehe)

Whatever, here is some pari/gp code if you want to try how this works, install pari and play with it... The ctrl+c was pressed after about 5 minutes.
? lucas(p)=my(m=1<<p-1, s=Mod(4,m)); for(i=3,p,s=s^2-2); s==0
%1 = (p)->my(m=1<<p-1,s=Mod(4,m));for(i=3,p,s=s^2-2);s==0
? cnt=1; for(p=3,1257787,if((l=lucas(p))>0,cnt++; print(cnt": 2^"p"-1 is prime"), printf("...%d...%c",p,13)))
2: 2^3-1 is prime
3: 2^5-1 is prime
4: 2^7-1 is prime
5: 2^13-1 is prime
6: 2^17-1 is prime
7: 2^19-1 is prime
8: 2^31-1 is prime
9: 2^61-1 is prime
10: 2^89-1 is prime
11: 2^107-1 is prime
12: 2^127-1 is prime
13: 2^521-1 is prime
14: 2^607-1 is prime
15: 2^1279-1 is prime
16: 2^2203-1 is prime
17: 2^2281-1 is prime
18: 2^3217-1 is prime
19: 2^4253-1 is prime
20: 2^4423-1 is prime
  ***   at top-level: ...=1;for(p=3,1257787,if((l=lucas(p))>0,cnt++;pr
  ***                                             ^--------------------
  ***   in function lucas: ...od(4,m));for(i=3,p,s=s^2-2);s==0
  ***                                                  ^-------
  ***   user interrupt after 5min, 12,328 ms
  ***   Break loop: <Return> to continue; 'break' to go back to GP prompt

Last fiddled with by LaurV on 2017-12-28 at 13:31
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