Quasiprimes

Quasiprimes are an important concept in the Theory of Numbers.

Albert Ingham was one of the leading British mathematicians of the 20th century. [1] He was able to prove the following theorem: If p is any prime greater than 13 then (p²-1)/24 is an integer that is not prime. Any integer that has this property but is not prime may be called an Ingham quasiprime.

The smallest quasiprime is 25, since (25²-1)/24 = 26 is not prime.

Ingham was also able to show that if n is a quasiprime then so is 2ⁿ-1. This implies that there are infinitely many quasiprimes. A much stronger result was proved in 2016: there are infinitely many integers n such that both n and n+2 are quasiprimes.