142 Jean-Marie De Koninck

2 057

• the number of pseudoprimes in base 2 smaller than 108 (see the number 245).

2 080

• the smallest number n 1 such that

γ(n)2|σ2(n);

the sequence of numbers

satisfying this property begins as follows: 1, 2 080, 2 100, 6 912, 16 800, 18 900,

21 600, 34 300, 52 000, 64 000, . . .

2 083

• the prime number which appears the most often as the

13th

prime factor of an

integer (see the number 199).

2 089

• the largest prime factor of the Mersenne number 229 − 1, whose complete fac-

torization is given by

229

− 1 = 233 · 1103 · 2089.

2 099

• the fourth prime number q such that

∑

p≤q

p is a multiple of 100: here this sum

is equal to 305 800 (see the number 563).

2 102 (= 2 · 1051)

• the 1

000th

number having exactly two distinct prime factors (see the number

184).

2 127

• the sixth number n such that 2n + n2 is prime (see the number 2 007).

2 131

• the second odd number k such that 2n + k is composite for all numbers n k

(see the number 773); in fact the smallest number n such that 2n + 2131 is

prime (if any exists !) is larger than 4 400.

2 133 (= 33 · 79)

• the second 2-hyperperfect number (see the number 21).