264 Jean-Marie De Koninck

556 160

• the seventh number n such that φ(n) + σ(n) = 3n (see the number 312).

559 940

• the smallest number n such that the decimal expansion of 2n contains ten

consecutive zeros, namely from the 94 170th decimal of 2n to the 94 179th (see

the number 53).

569 328

• the eighth number n such that φ(n) + σ(n) = 3n (see the number 312).

570 375

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

945).

575 119

• the smallest prime number q1 such that each number qi = 3qi−1 + 2 is prime

for i = 2, 3, . . . , 7: such a sequence of prime numbers is in some sense similar

to the Cunningham chains (see the number 1 122 659).

586 081

• the number of seven digit prime numbers (see the number 21).

586 951

• the smallest number n such that P (n) P (n + 1) . . . P (n + 9): here

586951 73369 21739 9467 1319 1193 1181 1091 677 29

(see the number 1 851).

590 226 (= 2 · 3 · 7 · 13 · 23 · 47)

• the tenth ideal number (see the number 390).