182 Jean-Marie De Koninck

9 567

• the only solution “SEND” to the first known cryptogram

SEND + MORE = MONEY,

9 567 + 1 085 = 10 652

(see the number 1 085).

9 587

• the smallest prime number that is preceded by 35 consecutive composite num-

bers; indeed, there are no prime numbers between 9 551 and 9 587.

9 592

• the number of prime numbers 100 000.

9 623

• the smallest prime factor of the Mersenne number

2283

− 1, whose complete

factorization is given by

2283

− 1 = 9623 · 68492481833 · P71.

9 689

• the exponent of the

21rst

Mersenne prime

29 689

− 1 (Gillies, 1963).

9 800

• the fourth powerful number n such that n + 1 is also powerful (see the number

288): here 9 800 =

23

·

52

·

72

and 9 801 =

34

·

112;

• the fifth solution w + s of the aligned houses problem (see the number 35).

9 801

• the sixth number n such that the binomial coeﬃcient

(

n

2

)

is a perfect square:

here

(9

801

2

)

= 6

9302

(see the number 289).

9 865

• the number of digits in the decimal expansion of the Fermat number

2215

+ 1.