# 1021

This number is a prime.

*p* = 1019 and 1021 are the largest known pair of twin primes where both *p*# + 1 and (*p*+2)# + 1 are primorial primes.

The largest prime date in a common year falling exactly in between a prime number (71) of remaining days and a prime number (293) of elapsed days is October 21 or 10/21. Note that 71293 is prime. [Beedassy]

The only prime formed from the concatenation of two semiprimes (10 and 21) whose prime factors consist of the four prime digits. [Silva]

The only four-digit emirp pair whose reversals each occur on a 12-hour clock is 10:21 and its reversal. [Punches]

Note that in the matrix product:

[ 1 0 ] [ 2 3 ] [ 2 3 ] = [ 2 1 ] [ 1 1 ] [ 5 7 ]1021 is prime, 2311 is prime, 2, 3, 5 and 7 are the first four primes (and incidentally, 2357 is prime). This is the only pair of 2-by-2 matrices with this property. [Hartley]

The least prime > 11 whose digit sum equals the number of digits. [Hasler]

The smallest prime whose sum of digits and digital length are squares. [Silva]

The smallest emirp that contains the digit 2. [Gaydos]

The smallest concave-convex prime. [Pol]

The smallest emirp which begins and ends with the same digit. [Silva]

The smallest emirp containing three consecutive digits. [Loungrides]

The smallest emirp formed from the concatenation of first four Fibonacci numbers, i.e., 0, 1, 1, 2. [Loungrides]

The smallest 4-digit prime (emirp) whose difference of the two left most digits (1 and 0) equals the difference of the two rightmost digits (2 and 1). [Loungrides]

The smallest term in the only case of four emirps, (1021, 3023, 7027, 9029), formed by inserting the same 2-digit number ab, between the digits of a 2-digit repdigit number dd, where d is each of the ending digits of a multi-digit prime, i.e., inserting 02 between the digits of 11, 33, 77, 99. [Loungrides]