Those Fascinating Numbers 381

130 370 767 029 135 901

• the 17th horse number (see the number 13).

150 094 635 296 999 121 (= 819)

• the largest number n whose sum of digits is equal to

9

√

n (see the number

3 904 305 912 313 344).

201 446 503 145 165 177

• the first Sierpinski number to have been discovered (by Sierpinski in 1960): a

number k such that k ·

2n

+ 1 is composite for each number n ≥ 1 is called a

Sierpinski number; see the number 78 557.

209 317 712 988 603 747

• the number of 19 digit prime numbers.

212 104 218 976 916 644 (= 22 · 72 · 11092 · 296632)

• the 1 000 000 000th powerful number (see the number 3 136).

234 057 667 276 344 607

• the number of prime numbers 1019 (an estimate due to Marc Del´eglise).

539 501 733 634 012 578 (= 2 · 37 · 11 · 13 · 192 · 23 · 31 · 37 · 41 · 472)

• the smallest number which is not a prime power, but which is divisible by

the sum of the sixth powers of its prime factors, namely by 19184230593 =

37

· 11 ·

192

·

472

(see the number 378); at least three other numbers

satisfy212

this property, namely 280 128 388 470 016 293 362 568 270,

560 320 704 841 008 416 047 743 000 and

20 497 203 366 427 937 245 153 868 828 160.

550 843 391 309 130 318 (= 2 · 3 · 7 · 71 · 103 · 61559 · 29 133 437)

• the ninth Giuga number (see the number 30).

212To obtain these numbers, one can proceed as follows. For each number n1 which is the product

of a combination of the first 25 prime numbers, set s = γ(m), where m =

∑

p|n1

p6,

and examine

if s|n1; if such is the case, one can conclude that the number n = n1 · m/s is such that

∑

p|n

p6

divides n.