Those Fascinating Numbers 175

7 314

• the smallest number n such that ω(n) = ω(n + 1) = 4: here 7 314 = 2 · 3 · 23 · 53

and 7 315 = 5 · 7 · 11 · 19 (see the number 230).

7 321

• the seventh prime number of the form

(x4

+

y4)/2

(see the number 41): here

7 321 =

(14

+

114)/2.

7 385

• the 15th Keith number (see the number 197).

7 425

• the fourth of the existing eight primitive non deficient numbers (see the number

945).

7 436

• the fourth number which does not produce a palindrome by the 196-algorithm

(see the number 196).

7 487

• the smallest prime factor of the Mersenne number

2197

− 1, whose complete

factorization is given by

2197

− 1 = 7487

·26828803997912886929710867041891989490486893845712448833.

7 517

• the 1

000th

prime power, namely here a prime number (see the number 419).

7 549

• the largest known prime number p such that p−k2 is composite for each number

k

√

p; the other known prime numbers satisfying this property are 2, 5, 13,

31, 37, 61, 127, 379, 439, 571, 829, 991, 1 549 and 3 319 (see also the number

367).