Those Fascinating Numbers 387

1 000 000 000 000 000 000 117

• the smallest 22 digit prime number.

1 180 591 620 717 411 303 424

• the largest known number n of the form n = 2k for which the sum of the digits

is equal to k: here

270

= 1 180 591 620 717 411 303 424; the only other known

number of this type is 32 =

25.

1 357 913 579 135 791 357 913

• the second prime number of the form 1357913579135 . . ., that is whose digits

are the odd numbers 1, 3, 5, 7 and 9, repeated: the smallest is 13.

1 791 562 810 662 585 767 521 (= 11·13·17·19·31·37·43·71·73·97·109·113·127)

• the smallest Carmichael number which is the product of 13 prime numbers (see

the number 41 041).

1 834 933 472 251 084 800 000

• the value of 1! · 2! · . . . · 9!.

2 361 183 241 434 822 606 848 (=

271)

• the largest known power of 2 which does not contain the digit 7 in its decimal

expansion (see David Gale [86]; see also the footnote tied to the number 71).

2 677 687 796 244 384 203 115

• the

20th

horse number (see the number 13).

3 508 125 906 290 858 798 171

• the tenth Hamilton number (see the number 923).

3 551 349 655 007 944 406 147

• the smallest prime number of the form n6 + 1 091, here with n = 3 906 (see the

number 3 906).

9 999 999 999 999 999 999 973

• the largest 22 digit prime number.