284 Jean-Marie De Koninck

2 744 210

• the ninth solution y of the Fermat-Pell equation

x2

−

2y2

= 1: here (x, y) =

(3880899, 2744210); see the number 99.

2 759 640

• one of the three numbers n such that the polynomial x5 −x±n can be factored:

the other two are n = 15 and n = 22 440: here x5 − x ± 2 759 640 = (x2 ± 12x +

377)(x3 ∓ 12x2 − 233x ± 7320) (see the number 22 440).

2 806 861

• the fourth prime number p such that 31p−1 ≡ 1 (mod p2) (see the number

79).

2 836 295

• the third number which can be written as the sum of the cubes of its prime

factors: 2 836 295 = 5 · 7 · 11 · 53 · 139 =

53

+

73

+

113

+

533

+

1393

(see the

number 378).

2 879 865

• the smallest Niven number n such that n + 90 is also a Niven number, while

no others are located in between (see the number 28 680).

2 890 625

• the smallest seven digit automorphic number: 2 890 6252 = 8 355 712 890 625

(see the number 76).

2 914 393

• the second and largest prime number p

232

such that

97p−1

≡ 1 (mod

p2)

(see Ribenboim [169], p. 347): the smallest is p = 7.

2 976 221

• the exponent of the

36th

Mersenne prime

22 976 221

− 1 discovered by Spencer

in 1997 using the programme developed by G.F. Woltman (see the number

1 398 269).