145

This number is a composite.

The 145th prime number is 829 and 145829 is prime. Note that 1 + 4 + 5 + 8 + 2 + 9 is the largest prime factor of 145. Note also that 145 is congruent to 1 mod(8, 2, 9) and (8! + 2! + 9!) - (1! + 4! + 5!) is prime. [Petersen]

145 = 1! + 4! + 5! = 5 x 29 and is the smallest semiprime with this property. [Bajpai]

Counting itself, this semiprime is the stem node of a digraph of a record 47 semiprimes where immediate descendants are formed by concatenation of prime factors in either order. [Merickel]

145 is the smallest number that occurs as the digit sum of both (2p−1)ᵖ⁻¹ + (p−1)ᵖ and (2p−1)ᵖ⁻¹ − (p−1)ᵖ for some prime p. For p = 19, these are 37¹⁸ ± 18¹⁹, and both have a digit sum of 145. Curiously, 145 is also the digit sum of both 37¹⁹ and 37¹⁹ + 18¹⁹. [Ahmed]