366 Jean-Marie De Koninck

1 968 188 556 461

• the smallest prime number which is followed by at least 600 consecutive compos-

ite numbers (in fact here by exactly 601 composite numbers); see the number

370 261.

2 094 447 251 857

• the seventh number having two representations as the sum of two co-prime

fourth powers:

2 094 447 251 857 =

12034

+

764

=

11764

+

6534

(see the number 635 318 657).

2 152 302 898 747

• the smallest strong pseudoprime in bases 2, 3, 5, 7 and 11 (Riesel [173], p. 91).

2 207 984 167 552 (= 587)

• the seventh number n 1 whose sum of digits is equal to

7

√

n (see the number

612 220 032).

2 404 879 675 441

• the 18th Euler number (see the number 272).

2 615 428 934 649

• the only number 2 which is equal to the sum of the factorials of its digits

in base 16: here 2 615 428 934 649 = [2, 6, 0, 15, 3, 11, 6, 6, 11, 15, 9]16 = 2! + 6! +

0!+15!+3!+11!+6!+6!+11!+15!+9! (see also the numbers 145 and 40 472).

2 682 923 295 390 (= 2 · 3 · 5 · 13 · 23 · 47 · 113 · 199 · 283)

• the 15th ideal number (see the number 390).

2 710 954 639 361

• the smallest prime factor of F13 =

2213

+ 1 (see the number 70 525 124 609).

2 733 834 545 701 (= 74 · 30893 · 36857)

• a 6-hyperperfect number, possibly the fifth (see the number 301).