Random pseudoprime: 759932492170846988701 is pseudoprime to bases 2, 3, 5, 7, 11, and 13. By the way: Is there a world record for "largest composite pseudoprime"?

Also: I forgot how to write a Fermat pseudoprime generator.

[QUOTE=3.14159;225001]Random pseudoprime: 759932492170846988701 is pseudoprime to bases 2, 3, 5, 7, 11, and 13. By the way: Is there a world record for "largest composite pseudoprime"?[/QUOTE]

Not really, you can generate them essentially as large as you like.

[QUOTE=3.14159;225001]Also: I forgot how to write a Fermat pseudoprime generator.[/QUOTE]

Depends on what you mean by "generator". Are you looking for a program that does the Fermat test? A program that generates all Fermat pseudoprimes in a range? A program that generates a Fermat pseudoprime at a given size? Something else?

[QUOTE=CRGreathouse]Not really, you can generate them essentially as large as you like.
[/QUOTE]

I see.

[QUOTE=CRGreathouse]Depends on what you mean by "generator". Are you looking for a program that does the Fermat test? A program that generates all Fermat pseudoprimes in a range? A program that generates a Fermat pseudoprime at a given size? Something else?
[/QUOTE]

A program that generates the Fermat pseudoprimes in a given range, that are pseudoprime to user-selected bases. (No need for a code snippet, I eventually remembered how to write it and saved it in the text document, along with the other functions.

[TEX]24m= 6np+(p-7)\right m=px+c [/TEX]
[TEX] 24m=6np-(p+7)\right m=px+c ? [/TEX]
[TEX]if(px+c==(4n-1)/3,(4\strike n -1)/3[/TEX]
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents

get this CRG ?

An interesting application error:
Whenever I input 25326001, it returns that it is a 7-SPRP, when it is in fact reported "composite" using base 7. I verified that it was an error on the app. Now I see that this is an unreliable app, as it returns results that are clearly wrong.

[QUOTE=3.14159;225036]A program that generates the Fermat pseudoprimes in a given range, that are pseudoprime to user-selected bases. (No need for a code snippet, I eventually remembered how to write it and saved it in the text document, along with the other functions.[/QUOTE]

Ah. Hard task!

[QUOTE=3.14159;225040]An interesting application error:
Whenever I input 25326001, it returns that it is a 7-SPRP, when it is in fact reported "composite" using base 7. I verified that it was an error on the app. Now I see that this is an unreliable app, as it returns results that are clearly wrong.[/QUOTE]

What script are you using to check? My isSPRP gives
[code]>isSPRP(25326001,7)
%1 = 0[/code]

[QUOTE=science_man_88;225037][TEX]24m= 6np+(p-7)\right m=px+c [/TEX]
[TEX] 24m=6np-(p+7)\right m=px+c ? [/TEX]
[TEX]if(px+c==(4n-1)/3,(4\strike n -1)/3[/TEX]
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents

get this CRG ?[/QUOTE]

sorry should be (4^n-1)/3 lol
oh and there shouldn't be 2 n equations lol.

[QUOTE=science_man_88;225037][TEX]24m= 6np+(p-7)\right m=px+c [/TEX]
[TEX] 24m=6np-(p+7)\right m=px+c ? [/TEX]
[TEX]if(px+c==(4n-1)/3,(4\strike n -1)/3[/TEX]
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents

get this CRG ?[/QUOTE]

Hmm. Unlike the diagrams, I feel like I'm close to understanding something. The first two lines are clearly related to your repeating theme,
[TEX]24m+7=p(6n\pm1)[/TEX].

The lines themselves seem to be statements of the division algorithm. The first says that if 24m+1 is of the form p(6n+1), then p(6n+1)/24 = px + c, that is, p(6n+1) leaves a remainder of c when divided by p.

But wait, it doesn't matter which of the first two lines I choose -- px + c is always m. So the first two lines say that 24m+7 is composite (assuming that n > 0 and p > 1) and the third line says that m is (4n-1)/3.

OK, so m = (4n-1)/3 means 3m+1 = 4n, so the third line is saying that [TEX]m\equiv1\pmod4[/TEX]. So let m = 4k+1, then 3(4k+1)+1=4n, so that n = 3k + 1.

The original composite is then 24m+7 = 24(4k + 1) + 7 = 96k + 31 and the Mersenne non-exponent is 2n+3 = 2(3k+1)+1=6k+3.

And indeed yes, this is correct: if k is a positive integer, then 6k+3 is not a Mersenne exponent. But this won't remove all bad exponents, of course.

[QUOTE=science_man_88;225047]sorry should be (4^n-1)/3 lol
oh and there shouldn't be 2 n equations lol.[/QUOTE]

Pity, since I just analyzed it without.

Re-write it with those corrections and I'll see what I can do.

[TEX]24m= 6tp+(p-7)\right m=px+c [/TEX]
[TEX] 24m=6tp-(p+7)\right m=px+c ? [/TEX]
[TEX]if(px+c==(4^n-1)/3,(4^\strike n -1)/3[/TEX]
for all remaining n [B]that create primes[/B] print(2*n+3) these are Mersenne prime exponents.