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)
Was "G 3719"
originally designed for those failing to extend OEIS
A390417?
The human race is petrified in stone for 3719 years in "Dr. Stone" by Riichiro Inagaki. [Yuki]