Quote from: Eli0t on July 17, 2013, 02:10:59 AM

Quote from: Vorksholk on July 17, 2013, 01:32:19 AM

Quote from: Eli0t on July 17, 2013, 12:49:16 AM

Quote from: Vorksholk on July 17, 2013, 12:27:21 AM

Quote from: Eli0t on July 17, 2013, 12:23:19 AM

-What purpose the sieve serves

In mathematics, the sieve of Eratosthenes, one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.

The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.

The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes (below 10 million or so)

awesome bounty btw i hope someone gets it

Yeah, during my short digging I did find the sieve of Eratosthenes, though your explanation was better than what I found. My main question with the sieve is, since we are finding very huge primes, what purpose this 'table of primes' serves the finding of large prime chains?

the sieve works by getting increasing more likely 'primes' by altering a value to be more likely prime, and the table is used as seeds for that 'winnowing' process.
You want to have a big table because the more you have, the more likely one of them will work for a given block.

This is really interesting! Mathematically, how does the sieve table work? Is one of the primes multiplied by a certain value and then changed in order to obtain a true prime? Also, what address do you want your 0.25 BTC to?

the prime chain is linked to the block header hash by requiring that its origin be divisible by the block header hash.
p_k/r is used to measure the difficulty of the chain. r is the Fermat test remainder of the next number in chain p_k
d = k + (p_k- r)/p_k

k is the prime chain length. d = difficulty if p_k passes probable primality tests then it should be considered as a chain of higher integral length.

my BTC addy is 13YGmE2CCAxWpAhqQSm5NVz9pU7Q4B22jm
thanks

Stellar, sent your 0.25 BTC

Cheers!!