Those Fascinating Numbers 385

48 698 490 414 981 559 698

• the second number which is not a fourth power, but which can be written as

the sum of the fourth powers of some of its prime factors: here

48 698 490 414 981 559 698 = 2 ·

34

· 7 · 13 · 17 · 157 · 83537 · 14816023

=

24

+

174

+

835374;

the smallest number satisfying this property is 107 827 277 891 825 604 (see the

number 870).

53 861 511 409 489 970 176 (=

9410)

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

10

√

n (see the number

13 744 803 133 596 058 624).

73 742 412 689 492 826 049 (=

9710)

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

10

√

n (see the number

13 744 803 133 596 058 624).

89 726 156 799 336 363 541

• the largest left truncatable prime number whose last digit is 1 (Gerry Myerson,

West Coast Number Theory Problems, 1999); see the number 73 939 133.

92 801 587 319 328 411 133

• the

19th

horse number (see the number 13).

99 999 999 999 999 999 989

• the largest 20 digit prime number.

100 000 000 000 000 000 039

• the smallest 21 digit prime number.

154 345 556 085 770 649 600 (= 215 · 35 · 52 · 72 · 11 · 13 · 17 · 19 · 31 · 43 · 257)

• the smallest 6-perfect number, that is a number n such that σ(n) = 6n (see the

number 6); it is believed that there are no more than 245 such numbers (see

R.K. Guy [104]).