# 281

This number is a prime. 281!/281# ± 1 are twin primes. Note that 281 is a prime of form n!3 + 1. [Luhn] Wilfred Whiteside of Houston, Texas, discovered the following 7-by-7 array in which 281 primes can be found:

``` 3 1 3 7 3 3 9
9 9 2 3 3 3 3
6 9 7 7 8 9 4
7 6 1 5 9 1 9
7 7 3 4 2 1 1
9 9 4 7 9 3 9
3 3 7 1 9 9 9.
``` The largest prime p such that (1!+2!+3!+4!+ ... +p!) - 2 is prime. [Capelle] 281 is the sum of consecutive primes up to 43. If we add consecutive primes up to 281, it too is prime (7699). Note that there are no other such primes with this behavior between 281 and 7699. [Poo Sung] The largest prime partial sum of number of irreducible diagrams (in the sense of perturbation expansion in quantum field theory: spinor case in 4 spacetime dimensions) with 2n nodes. [Post] 281 = 9*8 + 7*6 + 5*4 + 3*2 + 1 + 2*3 + 4*5 + 6*7 + 8*9. [Silva] The number of strong primes and the number of weak primes are equal at 281 (the 60th prime). [Honaker] The first multi-digit prime n that creates two compositorial primes, i.e., primes of form n!/n# - 1 and n!/n# + 1. Note that these primes are the terms of a twin prime pair. [Loungrides] Sum of the only known terms in the "dead school teacher" sequence, i.e., 66, 63, 57, 95. There are 281 triangular numbers on the 24-hour digital clock with seconds. [Gaydos] 281 and 283 are the smallest prime twins that are consecutive distinct digit numbers. [Gaydos] The existing partial copy of "The Code of Hammurabi" contains 281 laws, although the common belief is that there are more. There are 281 distinct ways to dissect a square into seven rectangles of equal area. [Descartes]

(There are 5 curios for this number that have not yet been approved by an editor.)