In Hardy & Littlewood's Partitio Numerorum III, Conjecture H is that every sufficiently large integer is either a square or the sum of a square and a prime. For n up to 3 million, the largest n that is not a square or a square plus a prime is n = 21679.
Is this in the literature? Has anyone tested beyond 3 million (I expect that they have)? Is there a specific conjecture as to what "sufficiently large" is here (is it greater than 21679)?