# 467

This number is a prime. (1!+2!+3!+ ... +n!) - 2 is divisible by this prime number p for all natural numbers n > p - 2. [Capelle] The smallest prime p in which the concatenation of p with the next prime remains prime throughout two steps of the same procedure. For example, 467 concatenated with the next prime (479) gives the prime 467479, and 467479 concatenated with the next prime (467491) gives the prime 467479467491. 467 is also the smallest whose successive concatenations remain prime throughout three steps. [De Geest and Post] The smallest prime whose digits form an acute-angle scalene triangle. [Loungrides] The number of full reptend primes less than 10,000. The only known prime p such that (130^p+1)/131 is prime. [Luen] 467 is the only known Pennington "Gap" prime, i.e., a prime number of form (2^p-1)*(2^(p-1))-(2^q-1)*(2^(q-1))-1, where p, q (p>q) are two adjacent Mersenne exponents (p=5 and q=3). It equals the prime number of integers between two successive perfect numbers, namely 28 and 496. If another exists, it will have more than 100,000 decimal digits. [Honaker]

(There are 2 curios for this number that have not yet been approved by an editor.)