3719

This number is a prime.

The smallest emirp formed by using all end digits of multidigit primes. [Tough]

The largest of four emirps each formed from two double-digit primes. The others are 1723, 1753, and 1789. [Loungrides]

The Gregorian year will not fall one day behind until the year 3719. [Jackson]

There are are 3719 different ways to arrange the set of twelve pentominoes into a rectangle (6-by-10, 5-by-12, 4-by-15, or 3-by-20), counting up to rotations and reflections. [Nie]

Of the 24 permutations of this prime there are 6 more primes - namely 3917, 7193, 1973, 9173, 9371 and 9731. [Tough]

Chebyshev's bias indicates that prime numbers up to n for any natural number n tend to end in 3 or 7 slightly more often than 1 or 9. [Nie]

Consider four ending digits of prime numbers, i.e., {1, 3, 7, 9}. The permutation {3, 7, 1, 9} occurs at 53, where the distinct frequencies of each of the four ending digits less than or equal to 53 can be written (high-to-low) as "3719", i.e., there are five 3s, four 7s, three 1s, two 9s. Question: At what prime p can we say that all 24 permutations of the ending digits have occurred? The sequence of primes leading to a solution begins 53, 239, 347, ... , corresponding to the first occurrence of {3, 7, 1 ,9}, {3, 7, 9, 1}, {7, 3, 1, 9}, etc. (See OEIS A390417)