Why not attach to a critical result a kind of computation fingerprint?
Say, compute parity/CRC-8/CRC-32/(whatever *fast* checksum, eg. first and last word) of a residue each 1/100/10000/(whatever seems reasonable) iterations, but send the checksums to a server only when claiming a prime.
That would definitely safe verification time in case of an error, and allow to locate a block of iterations where the error appeared.
Max
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