Those Fascinating Numbers 283

2 590 623

• the first of the three smallest consecutive numbers each of which is divisible

by a fifth power: here 2 590 623 =

35

· 7 · 1523, 2 590 624 =

25

· 73 · 1109 and

2 590 625 =

55

· 829 (see the number 1 375).

2 646 798

• the ninth (and possibly the largest) number n 9 such that n =

∑r

i=1

di, i where

d1, . . . , dr stand for the digits of n: here 2 646 798 = 21 +62 +43 +64 +75 +96 +87

(see the number 175).

2 657 333

• the third number which can be written in two distinct ways as the sum of

two co-prime numbers each with an index of composition ≥ 5: 2 657 333 =

27 + 312 · 5 = 55 + 215 · 34, each of these last four numbers having as index of

composition 7, 5.46252, 5 and 8.25538 respectively (see the number 371 549).

2 674 440

• the

14th

Catalan number (see the number 14).

2 677 889

• the smallest number of persistence 8 (see the number 679).

2 702 765

• the 12th Euler number (see the number 272).

2 704 900

• the fourth multiple of 100 such that the following 100 numbers include ex-

actly 17 prime numbers, namely 2704901, 2704903, 2704907, 2704909, 2704927,

2704931, 2704937, 2704939, 2704943, 2704957, 2704963, 2704969, 2704979,

2704981, 2704987, 2704993, 2704997 (see the number 400).

2 718 281

• the third prime number built from the first digits of the decimal expansion of

the Euler number e (see the number 271).