Those Fascinating Numbers 285

2 999 999

• the largest number n such that f6(n) n, where f6(n) = f6([d1, d2, . . . , dr]) =

d1 6 + d2 6 + . . . + dr 6, where d1, d2, . . . , dr stand for the digits of n.

3 020 626

• the fourth even number n such that

2n

≡ 2 (mod n); see the number 161 038.

3 021 377

• the exponent of the 37th Mersenne prime 23 021 377 −1 discovered by R. Clarkson

(a 19 year old student) in 1998 using the programme developed by G. Woltman

(see the number 1 398 269).

3 263 443

• the sixth voracious number (see the number 1 807).

3 290 624

• the smallest number n such that n and n + 1 each have ten prime factors

(counting their multiplicity); indeed, 3 290 624 = 29 · 6427 and 3 290 625 =

34 · 55 · 13 (see the number 135).

3 343 776

• the

11th

number n such that φ(n) + σ(n) = 3n (see the number 312).

3 345 408

• the 13th number n 1 such that φ(σ(n)) = n (see the number 128).

3 358 169

• the first term of the smallest sequence of 12 consecutive prime numbers all of

the form 4n + 1 (see the number 2 593).

3 370 501

• the sixth and largest solution x of the Bachet equation x2 + 999 = y3 (see the

number 251).