cp's OEIS Frontend

There are exactly 2668 eight-digit primes using digits 0-to-7 exactly once: here the smallest ones are given; cf. A109178 with the largest ones.

There are exactly 16 five-digit primes using the decimal digits 0 through 4 exactly once. There are exactly 2668 eight-digit primes using the digits 0 through 7 exactly once: A109177 (smallest ones), A109178 (largest ones).

This is a subsequence of A187796 = A109176 union A109177, which comprises all primes of that form (in decimal notation). - M. F. Hasler, Jan 06 2013

Starts with the 5-digit terms listed in A109176: There is no smaller prime of that form, since there is no odd number of that form with less than 3 digits, and those with digits {0,1,2} and {0,1,2,3} (as, e.g., 2013...) are all divisible by 3, thus composite.

For similar reasons, there cannot be terms with the 6 digits {0, ..., 5} or the 7 digits {0, ..., 6} (since 1 + ... + 5 (+ 6) is divisible by 3).

The 8-digit terms a(17)..a(2684) are also listed in A109177 and A109178 (in reverse order). Again, there are no 9- or 10-digit terms (since 0+1+...+8(+9) is divisible by 9). Therefore, the sequence has no terms beyond the 2684 terms < 76543210 listed in the b-file.

There are exactly 16 five-digit primes using decimal digits 0-to-4 exactly once: A109176 and 2668 eight-digit primes using each of 0-to-7 decimal digits exactly once: A109177, A109178. Cf. A094258.

Among 2668 eight-digit primes which use each of the decimal digits 0-to-7 just once, there are 102 pairs of mutually reversed primes. Here some smallest ones are given.