364 Jean-Marie De Koninck

824 633 702 441

• the first member of the twin prime pair which initiated the discovery in 1994

of a bug in the Intel chip; indeed, while computing the value of the

Brun209

constant

1

3

+

1

5

+

1

5

+

1

7

+

1

11

+

1

13

+ . . . +

1

p

+

1

p + 2

+ . . .

= 1.902160577783278 . . . ,

working with a computer using this Intel chip, Nicely observed that the values

of the reciprocals of the prime numbers 824 633 702 441 and 824 633 702 443 were

wrong starting with the tenth decimal (see James Glanz [90]).

865 363 202 000

• the

18th

powerful number n such that n + 1 is also powerful: here

865 363 202 000 =

24

·

53

·

112

·

312

·

612

and 865 363 202 001 =

34

·

412

·

25212

(see the number 288).

911 131 213 824

• the

36th

insolite number (see the number 111); it is the smallest insolite number

containing the digit 9.

999 999 999 989

• the largest 12 digit prime number.

1 000 000 000 039

• the smallest 13 digit prime number.

1 018 976 683 725 (= 33 · 52 · 72 · 11 · 13 · 17 · 19 · 23 · 29)

• the smallest odd number n such that σ(n) 3n; note that n = 945 is the

smallest odd number such that σ(n) 2n.

1 039 019 056 246 (= 2 · 317 · 1381 · 1186699)

• the 1 000 000 000 000th composite number (see the number 133).

209This

is only the conjectured value of the Brun constant. Indeed, Carl Pomerance observed that

no one has even yet proved that this constant is smaller than 2.