# Prime Bounty by Conjecture

**2 ^{57,885,161} − 1** (approaching 17.5 million digits). In order to illustrate the magnitude and historical importance of this discovery, a bounty of up to 2 LTC bounty can be claimed by the first post of a number-pairing (with proof

^{}) that meets the criteria of

**Goldbach's Conjecture**for the number

**2**

^{57,885,161}^{}. The 2 LTC bounty decays by 3% for each day that passes with no correct answer (iow, it's, at most, a month-long contest).

^{}Proof is required since there could be more than one answer (assuming there is one).

## Comments

Raise the bounty and I'll consider it.

Consider sharing the solution, that is.

@vivalafai True; it is a modest/meagre sum for such a remarkable achievement; however, Goldbach's Conjecture is a labour of love and I'd make every effort to have the solution listed in wikipedia and 'prime' websites with full-credit to the author. That was planned from the start though so, while it doesn't raise the bounty, perhaps it provides incentive. If it's bounty you seek, the $250,000 USD reward for the first 25,000,000+ digit prime is still on the table.

p.s. your nym.. Live the Dream?

@3gghead What I had in mind is actually not a proof of Goldbach, but a procedure on how to go about finding prime number pairings for the evens. I am thinking of two different methods, one which may be considered "cheating", because smaller primes are known a priori, but it is the easiest to program. The other involves making some statements about bounds on the sequence defined by the next prime minus its predecessor and interpolating it with the sequence of Mersenne primes. I am not being clear--I wish I could put more work into that problem at the moment. What are some of your thoughts?

257,885,161 − 1is prime, then2^{2}^{57,885,161}is also prime, and so on.^{-1}-1Clever nym.. not likely to be usurped by others. "Homage to CA" is on my list.

(regardless of radix) is not prime.

I'm inclined to agree with you regarding arbitrary testing of mersenne primes but it's such an easy approach I assumed "GIMPS" would have already claimed the bounty. The most recent prime is so much larger than its predecessors that finding the prime as the basis for the Goldbach pair is non-trivial.

As for the bounty problem, I've yet to ferret out a solution (which I was hoping to do by today) but, unlike a 'weak conjecture' solution, I'm inclined to believe the summed numbers closely straddle n * 0.5 (beoops.. spoiler). Ha, the "spoiler" could be a misdirect since 29+3 = 19+13 = 32. Since it's "Pi Day" here's one of the prime resources on the net though anyone trying to solve the problem has probably found this already.

btw.. 257,885,161 − 1

Right, what I wanted to do was write a script that uses known smaller primes and tests from 0.5*n down. One solution is sufficient for the problem...finding ALL pairs one would have to let the program run until it halts.