Thread for posting tiny primes

[3.14159]

Submissions: 242 * p(881)#² + 1 (5868 digits)

[3.14159]

Down to 37600 candidates..

20:19:15 37600 k's remaining. p=7270485000731 divides k=1907653

Let's see the odds:

ln(2^594800) = 412283.9429970554700..

Divide by 2; 206141.9714985277350..

The sieve efficiency, so far, is 26.6049431984462713172..

Dividing yields, the odds: 1 in 7748. Seems decent to me. I'll go a bit further.

[3.14159]

I should also organize some (personal) sieving params, for k * bⁿ + 1.

Level 1: ≤ 10⁶ (Small primes)
Level 2: 10⁶ to 10⁹ (Small primes)
Level 3: 10⁹ to 10¹² (Mid-size primes)
Level 4: 10¹² to 10¹³ (Large primes)
Level 5: ≥10¹³. (Large primes, only when b=2.)

And; the k's seem to be getting eliminated rather quickly. Still in sub-minute times.

[3.14159]

For aⁿ * q^x + 1 primes, where only one base is prime, the other base = 2 or any power of 2.

[3.14159]

Submissions: 2⁴²⁸ * 109⁹⁹⁶ + 1 (2159 digits)

Current progress: (k * 2⁵⁹⁴⁸⁰⁰ + 1)

00:03:23 37323 k's remaining. p=9047970928903 divides k=2275735

[3.14159]

01:35:23 37216 k's remaining. p=9781967722003 divides k=2213971

Final report on progress, will continue tomorrow..

[3.14159]

Personal record for second-kind Cunningham primes: 2641 * 1296¹⁹⁸ + 1 and 5282 * 1296¹⁹⁸ + 1 are both prime. (620 and 621 digits)

Nevermind; 1373 * 1296²³⁴ + 1 and 2746 * 1296²³⁴ + 1 are both prime, both at 732 digits.

[3.14159]

So far, my odds are now at 1 in 7623, for finding any primes. I've currently sieved out all candidates with divisors of 1-13 digits.

I recently eliminated 1730415 * 2⁵⁹⁴⁸⁰⁰ + 1. It was divisible by 11978969437139.

I've recently reached 1 in 27 candidates to be eliminated.

Also; Does anyone know how to make a simple script for testing primality of any k*n + c expression over a range of k and n? Similar to what the original PrimeForm allows?

[3.14159]

Also; I've saved myself about 2 days of testing time today.

[science_man_88]

Originally Posted by 3.14159

Also; Does anyone know how to make a simple script for testing primality of any k*n + c expression over a range of k and n? Similar to what the original PrimeForm allows?

Pisequence(kmin,kmax,nmin,nmax,c)=for(k=kmin,kmax,for(n=nmin,nmax,if(isprime(k*n+c),print(k"*"n"+"c))))

is this what you want ?

[3.14159]

Originally Posted by science_man_88

is this what you want ?

Not for PARI. I already have one, but thanks anyway.

I meant, for PFGW.

I intend to continue for the collection of primes for k * 1296ⁿ + 1; k = 1 to 10k. I've almost collected every small prime for this range. (< 1000 digits.) I'm up to about 983 digits.

I used Proth.exe for it all. I intend to continue until it becomes slow to the point where it is useless.