160 Jean-Marie De Koninck

4 151

• one of the seven numbers which can be written as the sum of the fifth powers

of its digits: 4 151 =

45

+

15

+

55

+

15

(see the number 4 150).

4 177

• the tenth prime number p such that (3p − 1)/2 is itself a prime number (see

the number 1 091).

4 179

• the smallest number n such that ω(n)+ω(n+1)+ω(n+2)+ω(n+3) = 13: here

4 179 = 3 · 7 · 199, 4 180 = 22 · 5 · 11 · 19, 4 181 = 37 · 113 and 4 182 = 2 · 3 · 17 · 41

(see the number 987).

4 181

• the smallest composite Fibonacci number whose rank is prime: F19 = 4 181 =

37 · 113.

4 253

• the exponent of the

19th

Mersenne prime

24 253

− 1 (Hurwitz, 1961).

4 273

• the smallest number n requiring ten iterations of the σI (n) function in order

to reach 1 (see the number 193).

4 297

• the prime number which appears the most often as the

14th

prime factor of an

integer (see the number 199);

• the smallest prime number p such that p + 30 is prime and such that each

number between p and p + 30 is composite (see the number 139);

• the 14th prime number pk such that p1p2 . . . pk − 1 is prime (see the number

317).

4 316

• the second solution of σ2(n) = σ2(n + 8) (see the number 860).