# 48

This number is a composite.

If n is greater than or equal to 48, then there exists a prime between n and 9n/8, exclusive.

The smallest even number that can be expressed as a sum of two primes in five different ways (5 + 43, 7 + 41, 11 + 37, 17 + 31, 19 + 29). [Rivera]

48 = π(4)! * π(8)! [Firoozbakht]

48!2 + prime(84) is prime. [Farzannia]

48 is the smallest number such that (7^48+48) and (7^48-48) are both prime. [Bajpai]

The smallest possible sum for a set of four distinct primes such that the sum of any three is prime: {5, 7, 17, 19}.

Questions: Is there a prime quadruplet (of the form {p, p+2, p+6, p+8}) with this property? (Click here for answer.) How about prime sextuplets, where the sum of any five are prime? (Click here for answer.) Or greater admissible prime constellations (k-tuples) such that the sum of any k-1 primes is prime? Update: Jens Kruse Andersen has found that due to divisibility by small primes, there is no k from 7 to 50 for which there exists a prime k-tuplet such that the sum of any k-1 is prime.

7^48+48 is the largest non-titanic prime of form 7^n+n. [Loungrides]

(There are 6 curios for this number that have not yet been approved by an editor.)