[QUOTE=3.14159;223452]Well, if you insist, I used 1/(ln(x)-1). That gave me about 1 in 92282. Eliminating multiples of 2 and 3 gives 1 in 30760. But it's actually closer to 1 in 30761.[/QUOTE]

How/why did you eliminate the multiple of 3?

[QUOTE=axn]How/why did you eliminate the multiple of 3?
[/QUOTE]

@Axn: Because I wished to increase the chances of success, and I've also already found a prime for that range: 207408 * 77906[sup]8192[/sup] + 1 (40078 digits)

[QUOTE=3.14159;223466]@Axn: Because I wished to increase the chances of success, and I've also already found a prime for that range: 207408 * 77906[sup]8192[/sup] + 1 (40078 digits)[/QUOTE]

I meant, what was the mathematical basis for accounting for 3 in the calculation of odds?

[QUOTE=axn]I meant, what was the mathematical basis for accounting for 3 in the calculation of odds?
[/QUOTE]

Why not? Only odd integers are considered for testing, and the multiples of three are unnecessary, because they're easy to get rid of. Why should they [B]not[/B] be accounted for?

[QUOTE=3.14159;223470]Why not? Only odd integers are considered for testing, and the multiples of three are unnecessary, because they're easy to get rid of. Why should they [B]not[/B] be accounted for?[/QUOTE]

You can remove multiples of 2 because your numbers are all odd. You can't remove mutiples of 3 because some of your numbers are divisible by 3. (Sure, you can trial-divide as high as you like, but that on;y gives you the answers faster, it doesn't increase the number of primes.)

[QUOTE=CRGreathouse]You can remove multiples of 2 because your numbers are all odd. You can't remove mutiples of 3 because some of your numbers are divisible by 3. (Sure, you can trial-divide as high as you like, but that on;y gives you the answers faster, it doesn't increase the number of primes.)
[/QUOTE]

Why can't I remove multiples of three? Primes are either 6n + 1 or 6n - 1. It's completely acceptable to remove multiples of 2 and 3, including odd multiples of three.

Also: Numbers where (7[sup]n[/sup] -1)/6 are prime: 5, 13, 131, 149, 1699, etc..

[QUOTE=3.14159;223479]Why can't I remove multiples of three? Primes are either 6n + 1 or 6n - 1. It's completely acceptable to remove multiples of 2 and 3, including odd multiples of three.[/QUOTE]

That has no bearing here. No numbers of the form k * 6^n + 1 are divisible by 2 or 3 so we can remove 2 and 3 when calculating the likelihood of a random number of that form being prime. No numbers of the form k * 77906^n + 1 are divisible by 2 or 38953, but some are divisible by 3 (e.g., 5*77906^8192+1).

[QUOTE=3.14159;223479]Numbers where (7[sup]n[/sup] -1)/6 are prime: 5, 13, 131, 149, 1699, etc..[/QUOTE]

That's Sloane's [url=http://oeis.org/classic/A004063]A004063[/url]. It continues 14221, 35201, 126037, 371669, ....

any help for elimination ?
 

[CODE](09:41) gp > forprime(p=5,100,for(n=1,p,if((p*n)%6==5,print1(n",");if(n==p-4 || n==p-2,print("_"p)))))
1,_5
5,_7
1,7,_11
5,11,_13
1,7,13,_17
5,11,17,_19
1,7,13,19,_23
1,7,13,19,25,_29
5,11,17,23,29,_31
5,11,17,23,29,35,_37
1,7,13,19,25,31,37,_41
5,11,17,23,29,35,41,_43
1,7,13,19,25,31,37,43,_47
1,7,13,19,25,31,37,43,49,_53
1,7,13,19,25,31,37,43,49,55,_59
5,11,17,23,29,35,41,47,53,59,_61
5,11,17,23,29,35,41,47,53,59,65,_67
1,7,13,19,25,31,37,43,49,55,61,67,_71
5,11,17,23,29,35,41,47,53,59,65,71,_73
5,11,17,23,29,35,41,47,53,59,65,71,77,_79
1,7,13,19,25,31,37,43,49,55,61,67,73,79,_83
1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,_89
5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,_97
(09:42) gp > forprime(p=5,100,for(n=1,p,if((p*n)%6==1,print1(n",");if(n==p,print("_"p)))))
5,_5
1,7,_7
5,11,_11
1,7,13,_13
5,11,17,_17
1,7,13,19,_19
5,11,17,23,_23
5,11,17,23,29,_29
1,7,13,19,25,31,_31
1,7,13,19,25,31,37,_37
5,11,17,23,29,35,41,_41
1,7,13,19,25,31,37,43,_43
5,11,17,23,29,35,41,47,_47
5,11,17,23,29,35,41,47,53,_53
5,11,17,23,29,35,41,47,53,59,_59
1,7,13,19,25,31,37,43,49,55,61,_61
1,7,13,19,25,31,37,43,49,55,61,67,_67
5,11,17,23,29,35,41,47,53,59,65,71,_71
1,7,13,19,25,31,37,43,49,55,61,67,73,_73
1,7,13,19,25,31,37,43,49,55,61,67,73,79,_79
5,11,17,23,29,35,41,47,53,59,65,71,77,83,_83
5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,_89
1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,_97[/CODE]

of course all this means is take (6*n+/-1)*p(a prime) as a subsequence that can't contain primes.

can we tell when 24n+7 wouldn't hit one of these ? if so maybe we can use that to help with speeding up the Mersenne prime search.

[QUOTE=science_man_88;223585]can we tell when 24n+7 wouldn't hit one of these ? if so maybe we can use that to help with speeding up the Mersenne prime search.[/QUOTE]

What does this mean?

[QUOTE=CRGreathouse;223589]What does this mean?[/QUOTE]

according to every person I know all mersenne primes>7 are 24n+7

since every (6n+/-1)*p number is a multiple of a number they can't be prime so if 24n+7 hits one it's not prime can we use this to predict which n for 24n+7 are prime and which ones are Mersenne primes ?