[QUOTE=CRGreathouse]Since Pi's not allowed to participate and no one else has stepped forward, I'll submit 1 * 2^2 - 1 = 3 for #20 and #21 and 3 = 5 - 2 for #22. Primality certificates available on request.
[/QUOTE]

Always going with the smallest examples. What exponents are you up to for your 2^n - 2293 search?

Also: I'll get to work on b = 251-500 for k-b-b's.

[QUOTE=science_man_88;227665]turn this into vectors:

[CODE]for(s=1,50,for(x=s,20000000*s,if(isprime(x),print1(x","));x=x*2);print("<--"s))[/CODE]

then compare with the exponents of Mersenne primes.

some don't fit them so we could say they may never hit them. if we can figure this out we can use it like a sieve.[/QUOTE]

So you're starting at some s and then looking at primes of the form 2^k * (s+1) - 1 for k = 0..24. What are you doing with them? What do you mean by comparing them with the exponents of Mersenne primes?

[QUOTE=CRGreathouse;227670]So you're starting at some s and then looking at primes of the form 2^k * (s+1) - 1 for k = 0..24. What are you doing with them? What do you mean by comparing them with the exponents of Mersenne primes?[/QUOTE]

check out s=11 up to the limit of known exponents for Mersenne primes they all aren't in it. so far about 1/3 of all the numbers checked up to 27 have sequences that seem to work like that so far.

[QUOTE=3.14159;227669]Always going with the smallest examples. What exponents are you up to for your 2^n - 2293 search?[/QUOTE]

Once I close the gap between my disjoint work assignments I'll be up to 920,000. But I still have some work in the lower 700,000s.

[QUOTE=CRGreathouse]Once I close the gap between my disjoint work assignments I'll be up to 920,000. But I still have some work in the lower 700,000s.
[/QUOTE]

Excellent. I'm nearing b = 300.

So, I've covered every prime under 760 digits so far.

Also: There seems to be a roundoff bug with b = 308 in between 3408 and 4870.

Is this just me?

[QUOTE=science_man_88;227671]check out s=11 up to the limit of known exponents for Mersenne primes they all aren't in it. so far about 1/3 of all the numbers checked up to 27 have sequences that seem to work like that so far.[/QUOTE]

I can write out the numbers for s = 11, but what do I do with them?

[QUOTE=3.14159;227675]Also: There seems to be a roundoff bug with b = 308 in between 3408 and 4870.[/QUOTE]

A roundoff bug in what?

@CRG: Can you make a quick script that asks NewPGen to sieve for a certain base-range?

[QUOTE=CRGreathouse]A roundoff bug in what?
[/QUOTE]

PFGW gets a roundoff bug, something to do with 0.5 > 0.45

This only happens where b = 308; k = 3408 to 4870.

[quote=3.14159;227680]
PFGW gets a roundoff bug, something to do with 0.5 > 0.45

This only happens where b = 308; k = 3408 to 4870.[/quote]
Can you post the details of the bug here? I've run into these myself in the past and if it's the kind of bug I'm thinking of, the PFGW program developer wants to hear about these.

[QUOTE=CRGreathouse;227678]I can write out the numbers for s = 11, but what do I do with them?[/QUOTE]

if you check the primes in this sequence out until the exponent of the largest Mersenne prime confirmed you'll see they are all prime for which 2^s-1 is not prime.

same with the others highlighted in red.

the numbers in orange mean that the sequence is part of another already highlighted in red.

[QUOTE=Matt]Can you post the details of the bug here? I've run into these myself in the past and if it's the kind of bug I'm thinking of, the PFGW program developer wants to hear about these.
[/QUOTE]

[code]Error occuring in PFGW at Mon Aug 30 10:54:47 2010
Expr = 3460*308^308+1
Detected in MAXERR>0.45 (round off check) in prp_using_gwnum
Iteration: 75/2557 ERROR: ROUND OFF 0.5>0.45
PFGW will automatically rerun the test with -a1[/code]