A108880 Alphabetically earliest number that is a product of exactly n primes.

8018018851, 8000000018, 8, 8018000018, 8018018886, 8018018085, 8018018808, 8000000008, 8018018000, 8018018048, 8018018816, 8018018176, 8018808000, 8018808832, 8018000000, 8018018304, 8018887680, 8018804736, 8018853888

Offset: 1

Author

Jonathan Vos Post, Jul 14 2005

Keywords

• nonn
• word

Comments

Conway and Guy note that 8018018851 is, alphabetically, the first prime number in the American system of large number terminology and term this "Knuth's number." We have "eight billion" alphabetically before "eighteen" or "eighty."

Examples

			n Alphabetically first n-almost prime
1 8018018851
2 8000000018 = 2 * 4000000009
3 8 = 2^3
4 8018000018 = 2 * 7 * 97 * 5904271
5 8018018886 = 2 * 3 * 19 * 6661 * 10559
6 8018018085 = 3 * 5 * 7 * 11 * 163 * 42589
7 8018018808 = 2^3 * 3 * 31 * 2161 * 4987
8 8000000008 = 2^3 * 7 * 11 * 13 * 19 * 52579
9 8018018000 = 2^4 * 5^3 * 127 * 31567
10 8018018048 = 2^8 * 43 * 728381
		

References

• Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 15, 1996.

Links

• Eric Weisstein's World of Mathematics, Almost Prime.

Crossrefs

Cf. A000052.

Extensions

Corrected and extended by Ray Chandler, Jul 25 2005

Definition clarified by N. J. A. Sloane, Sep 27 2011