Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known?

In mathematics, is there any conjecture about the existence of an object that was proven to exist but that has not been explicitly constructed to this day? Here object could be any mathematical object, such as a number, function, algorithm, or even proof.

Answer

It is known that there is an even integer n246 such that there are infinitely many primes p such that the next prime is p+n, but there is no specific n which has been proved to work (although everyone believes that every even n2 actually works).

Attribution
Source : Link , Question Author : lone student , Answer Author : Gerry Myerson

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