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good primes
A prime pn such that pn2 > pn-ipn+i for every 0 < i < n. more

The first 600 good primes :

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 68658 values, from 5 to 199968539).

n\r 0  1
2068658 2
303321235446 3
4034006034652 4
5117976193731521416094 5
603321200035446 6
70103401203311058123181049812411 7
8017033017340016973017312 8
9011073118110111841187801095511757 9
1001797601521401019373016094 10
1117090747666067162603775936604714762666676

A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.