This number is a composite.
π(!4) = 4, where !4 denotes subfactorial 4. [Gupta]
The smallest composite number.
18 99 86 61 66 81 98 19 91 16 69 88 89 68 11 96A 4-by-4 magic square displaying 4 primes. Note that the same occurs if rotated 180 degrees about the center of the square's plane.
Let n be an integer, and let C(n) be the number of ways n can be written as the sum of two primes. The numbers, C(n) are called Goldbach numbers. E.g., C(34) = 4 because 34 can be written as 3 + 31, 5 + 29, 11 + 23, and 17 + 17.
There is only one solution. [Mensa]* * * x * * --------- * * * * * * * * ----------- * * * * *
In the movie "Die Hard with a Vengeance", Bruce Willis must measure 4 litres of water using two containers one with a capacity of 3 litres and the other with 5 litres. This problem can be solved by the Euclidean algorithm since 3 and 5 are mutually prime. [Poo Sung]
1!1 +2!2 + 3!3 + 4!4 is prime. [Poo Sung]
44 - 4! + 1 is prime. [Luhn]
There are 4 two-digit primes formed by concatenation of prime digits. [Silva]
4 is the exact number of one-digit primes. [Patterson]
Four fours raised to the fourth power plus one is prime. I.e., 4444^4+1 is prime. [Opao]
4 fives plus five 4's is prime. [Opao]
The largest value for n less than 105, such that p = 2n + 3n is prime. [Opao]
4 is the largest number m such that prime(m) = sigma(m). [Firoozbakht]
4444^(4*4) + 4/4 is prime with prime length 4*4*4-4-4/4. [Memar]
4 is the smallest number n such that n and n! are product of factorials of primes (4 = 2!2! and 4! = 2!2!3!). [Capelle]
4 is the smallest number between twin primes. [Silva]
The only semiprime expressed by a prime p in two ways: p^2 and p+p. [Silva]
The number of 4-digit primes formed from the first 4 odd digits. [Silva]
4!!-3!!+2!!-1!! is a 4!-digit prime. [Silva]
There are 4 known positive integers n such that the sum of all primes smaller or equal to n divides n(n+1)/2. This sum also divides the sum of all nonprimes smaller or equal to n. Note that 4 is the smallest positive integer with this property. [Capelle]
The only known number n such that prime(n)^prime(n) - π(n) is prime. [Firoozbakht]
4 is the number of primes formed from 4 digits summing up to 4 [Silva]
The 4th prime that gives primes in translation twice from bases 2 and 3 to base 10 is the first to do it once from base 4. The 44th is the first to do it twice, and both begin with 234 in base ten (234099253 and 2348568403). [Merickel]
(4!) = !4. [Wesolowski]
The only digit that forms a prime with the previous digit (43). [Silva]
The smallest brilliant number. Brilliant numbers, as defined by Peter Wallrodt, are numbers with two prime factors of the same length (in decimal notation). These numbers are generally used for cryptographic purposes and for testing the performance of prime factoring programs. [Alpern]
4 is the number of 4-digit primes formed from the first 4 natural numbers: 1423, 2143, 2341, 4231. [Silva]