200 Jean-Marie De Koninck
where stands for a ν digit prime number, while is a ν digit composite
number158.
19 937
the exponent of the 24th Mersenne prime 219 937 1 (Tuckerman, 1971).
19 999
the largest number n such that f4(n) n, where f4(n) = f4([d1, d2, . . . , dr]) =
d1 4 + d2 4 + . . . + dr 4, where d1, d2, . . . , dr stand for the digits of n.
20 154
the smallest number n such that σ(n), σ(n +1), σ(n +2), σ(n +3) and σ(n + 4)
have the same prime factors, namely here 2, 3, 5 and 7: the sequence of num-
bers satisfying this property begins as follows: 20 154, 29 395, 214 195, 764 392,
768 594, . . . (see the number 3 777).
20 160
the
23rd
highly composite number (see the number 180).
20 161
the smallest number n having the property that each number n can be
written as the sum of two abundant numbers (C.S. Ogilvy and J.T. Anderson
[155]).
20 201
the smallest prime number equally distant, by a distance of 18, from the
preceding and following prime numbers: p2284 = 20 183, p2285 = 20 201 and
p2286 = 20 219.
20 440
the eighth number n such that σ(φ(n)) = n (see the number 744).
20 496
the only solution n
108
of σ(n) = 3n + 16.
158The
largest known prime of the form
10n
+ 1 is 101; one easily proves that if
10n
+ 1 is prime, n
must be a power of 2; but since one can easily check, using a computer, that
102k
+ 1 is composite
for 2 k 16, it follows that 10n + 1 is composite for 3 n 131 071 = 217 1.
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