1733

This number is a prime.

The smallest prime (also an emirp) p such that p and p^3 contain all digits from 0 to 9. [Gupta]

The smallest diagonal emirp. (A diagonal prime is a prime of n^2 digits (n > 1) arranged left-right, top-down in a n-by-n matrix, where the diagonals are also prime in each direction). [Loungrides]

The smallest emirp whose alternate digits (1733) segregate and reunite to form two "daughter" emirps (13 ; 73). [Beedassy]

(1733, 3371) is the only pair of 4-digit emirps formed by inserting an emirp between the digits of another emirp, i.e., inserting the emirp 73 between the digits of emirp 13 and the emirp 37 between the digits of emirp 31. [Loungrides]

A prime congruent to 5 (mod 12) followed by a gap of size 144 to the next prime congruent to 5 (mod 12) which is 1877. Note that a bigger gap between consecutive primes congruent to 5 (mod 12) does not occur until the gap of size 156 between 16673 and 16829. [Nie]

The smallest positive integer for which the sum of the different primes that are substrings of its digits (3+7+17+73+173+733) equals or exceeds one thousand. [Gaydos]