Those Fascinating Numbers 305

23 592 593

• the smallest prime number q such that

∑

p≤q

p is divisible by 9 699 690 (=

2 · 3 · 5 · 7 · 11 · 13 · 17 · 19): here this sum is equal to 16 904 658 530 760 (see the

number 269).

24 036 583

• the exponent of the 41rst Mersenne prime 224 036 583 − 1 (a 7 235 733 digit num-

ber) discovered by Michael Shafer on May 15, 2004, using the programme

developed by G. Woltman (see the number 1 398 269).

24 151 040

• the smallest number n such that n and n + 1 are both divisible by a tenth

power: here 24 151 040 =

210

· 5 · 53 · 89 and 24 151 041 =

310

· 409 (see the

number 1 215).

24 208 144

• the largest number n such that P

(n2+1)

100: here

n2+1

=

293·372·53·612·89:

this is a result due to F. Luca [127].

24 678 050

• the smallest number n 1 which is equal to the sum of the eighth powers of

its digits: the only other numbers satisfying this property are 24 678 051 and

88 593 477.

24 678 051

• the second number n 1 which is equal to the sum of the eighth powers of its

digits (see the number 24 678 050).

24 883 200

• the value of 1! · 2! · . . . · 6! .

25 153 757 (=

2933)

• the 1 000th 3-powerful number (see the number 216).

25 326 001

• the smallest strong pseudoprime in bases 2, 3 and 5.