Those Fascinating Numbers 183
9 871
the largest prime number with four distinct digits; if qk stands for the largest
prime number made up of exactly k distinct digits, then q1 = 7, q2 = 97,
q3 = 983, q4 = 9 871, q5 = 98 731, q6 = 987 631, q7 = 9 876 413, q8 = 98 765 431
and q9 = 987 654 103; it is clear that q10 does not exist (see the number 1 039
for the similar question for the smallest prime number with k distinct digits).
9 901
one of the only two prime numbers p (the other one is 101) satisfying the
property154 that any number of the form abcdefabcdef is divisible by p.
9 941
the exponent of the
22nd
Mersenne prime
29 941
1 (Gillies, 1963).
9 973
the largest four digit prime number.
10 007
the smallest five digit prime number.
10 080
the
21rst
highly composite number (see the number 180).
10 223
the smallest candidate still “suspected” of being a Sierpinski number (see the
number 78 557).
10 243
the smallest prime number made of five distinct digits (see the number 1 039).
10 305 (= 32 · 5 · 229)
the smallest number n which allows the sum
m≤n
Ω(m)=4
1
m
to exceed 1; the smallest
number that allows this sum to exceed 2 is 1 799 938.
154To
obtain this result, see the footnote tied to the number 9091, observing that 1 000 001 =
101 · 9901.
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