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.
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