Thread for posting tiny primes

[science_man_88]

because I would never know when all candidates end so I could never stop.

[CRGreathouse]

Originally Posted by science_man_88

because I would never know when all candidates end so I could never stop.

What does that even mean? "when all candidates end"


OK, maybe I need to find something easier, or at least different. How about this: you know how to calculate the odds of finding 0 primes with a given N and L. Can you create a function that reverses this? Say someone wants to sieve a range to a given L such that the range contains 0 primes with probability 1% (that is, the range is 99% likely to have primes).

[science_man_88]

well the probability that a candidate isn't prime is the opposite to if it is so reverse the fraction:

(17:36) gp > poisson3(N,t,n) = n!/(((t/log(N))^n)*exp(-(t/log(N))))
%260 = (N,t,n)->n!/(((t/log(N))^n)*exp(-(t/log(N))))

[CRGreathouse]

I was looking for a function that, given a probability p (and N, t, L), would give an n such that

estimatePrimes(N,t,n,L)

is 1 - p.

[3.14159]

Submissions: 37092 * 56087²⁸⁹⁰ + 1 (13729 digits)

Prime with prime number of digits.

Qualified for item 5.

[science_man_88]

if we could reverse engineer the first to find n we won't need to use L

[science_man_88]

did I mention the hard part is getting the last n out of the logarithm lol

[CRGreathouse]

Originally Posted by science_man_88

if we could reverse engineer the first to find n we won't need to use L

No, because you get different n depending on L.

Suppose N = 10^100. If L < 2 then n is 1064: you need to pick 1064 numbers near a googol to find a prime with 99% certainty. If L = 1000, then n is 87: you don't need to pick nearly so many numbers if you know that none have prime divisors smaller than a thousand.

[3.14159]

Is the above the code for Charles's (grammatical error?) request?

[3.14159]

Originally Posted by Charles

Suppose N = 10^100. If L < 2 then n is 1064: you need to pick 1064 numbers near a googol to find a prime with 99% certainty. If L = 1000, then n is 87: you don't need to pick nearly so many numbers if you know that none have prime divisors smaller than a thousand.

How about if I knew the numbers in question had no divisors smaller than 167772161?

[CRGreathouse]

Originally Posted by 3.14159

How about if I knew the numbers in question had no divisors smaller than 167772161?

Maybe you can ask sm that question once he finishes the script!

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