128 Jean-Marie De Koninck

1 429

• the largest known number of the form 1 + 4p1p2 . . . pk: here

1429 =

√

1 + 4 · 2 · 3 · 5 · 7 · 11 · 13 · 17; the only known numbers of this form

are 3, 5, 11, 29 and 1 429;

• the smallest prime number p such that p − 1 and p + 1 each have exactly four

distinct prime factors: here 1 428 = 22 · 3 · 7 · 17 and 1 430 = 2 · 5 · 11 · 13 (see

the number 131).

1 430

• the eighth Catalan number (see the number 14).

1 433

• the smallest prime divisor of a Mersenne number (namely

2179

−1) which is such

that the following prime number, namely 1 439, is also a divisor of a Mersenne

number (namely

2719

− 1); the only other known prime number satisfying this

property is 6 079.

1 439

• the smallest prime factor of the Mersenne number

2719

− 1, whose complete

factorization is given by

2719

− 1 = 1439 · 772207

·737572843389436536903316910033561929012829990389769 · P157.

1 441

• the smallest number n 2 which is equal to the sum of the factorials of its

digits in base 15: here 1 441 = [6, 6, 1]15 = 6! + 6! + 1!; the only numbers with

this property are 1, 2, 1 441 and 1 442 (see the number 145).

1 442

• the largest number which is equal to the sum of the factorials of its digits in

base 15: here 1 442 = [6, 6, 2]15 = 6! + 6! + 2! (see the number 1 441).