Those Fascinating Numbers 369

9 746 347 772 161 (= 7 · 11 · 13 · 17 · 19 · 31 · 37 · 41 · 641)

• the smallest Carmichael number which is the product of nine prime numbers

(see the number 41 041).

9 999 999 999 971

• the largest 13 digit prime number.

10 000 000 000 037

• the smallest 14 digit prime number.

10 358 018 863 853 (= 8837 · 1172119369)

• the 10 000 000 000

000th

composite number (see the number 133).

10 641 342 970 443

• the

14th

horse number (see the number 13).

10 650 056 950 807

• the seventh voracious number (see the number 1 807).

11 111 111 114 112

• the

41rst

insolite number (see the number 111).

11 410 337 850 553

• the first term of an arithmetic progression of prime numbers of length 22;

indeed, the numbers

11 410 337 850 553 + 4 609 098 694 200 · k, with k = 0, 1, 2, . . . , 21,

represent a sequence of 22 prime numbers in arithmetic progression (obtained

by Pritchard and al. in 1993); the sequence of numbers

376 859 931 192 959 + 18 549 279 769 020 · k, with k = 0, 1, 2, . . . , 21

(obtained by M. Frind in 2003) is also a sequence of 22 prime numbers in arith-

metic progression210.

210Recently,

Ben Green and Terence Tao [97] proved that there are arbitrarily long sequences of

prime numbers in arithmetic progression; it is an existence proof and not a proof by construction.