Those Fascinating Numbers 379

11 117 311 111 311 111

• the second odd insolite number which is not of the form 11 . . . 1.

11 131 117 111 113 111

• the third odd insolite number which is not of the form 11 . . . 1.

11 721 060 349 748 875 (=

53

·

1813

·

2513)

• the 1 000

000th

3-powerful number (see the number 216).

12 345 678 987 654 321

• the square of 111 111 111.

13 111 131 117 111 111

• the fourth odd insolite number which is not of the form 11 . . . 1.

14 737 133 470 010 574 (= 2 · 3 · 7 · 71 · 103 · 67213 · 713 863)

• the eighth Giuga number (see the number 30).

17 111 113 131 111 111

• the fifth odd insolite number which is not of the form 11 . . . 1.

22 114 397 130 086 627

• the number of 18 digit prime numbers.

22 439 962 446 379 651

• the smallest prime number p such that p + 1000 is prime and such that each

number between p and p + 1000 is composite (see the number 396 733): this

prime number p was discovered in 2003 by Nyman & Nicely [154].

26 584 448 904 822 018

• the smallest number which is not an eighth power, but which can be written

as the sum of the eighth powers of some of its prime factors: here

26 584 448 904 822 018 = 2 · 3 · 7 · 17 · 19 · 113 · 912733109 =

28

+

178

+

1138

(see the number 870); at least one more number satisfies this property, namely

210913096528905026899530575850386805453832507856329770499303938.