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Composite numbers (Posted on 2003-03-05) Difficulty: 3 of 5
Find 2000 consecutive composite numbers.

(Of course you can't do this by trial and error alone)

For those who do not know what a composite number is, it is any integer greater than 1 that is not prime. (4, 6, 8, 9, ...)

See The Solution Submitted by Anoop    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): Smaller solution? | Comment 14 of 22 |
(In reply to re(2): Smaller solution? by Charlie)

and continues...
( 401 1203)( 409 1227)( 419 1257)( 421 1263)( 431 1293)( 433 1299)
( 439 1317)( 443 1329)( 449 1347)( 457 1371)( 461 1383)( 463 1389)
( 467 1401)( 479 1437)( 487 1461)( 491 1473)( 499 1497)( 503 1006)
( 509 1018)( 521 1042)( 523 1046)( 541 1082)( 547 1094)( 557 1114)
( 563 1126)( 569 1138)( 571 1142)( 577 1154)( 587 1174)( 593 1186)
( 599 1198)( 601 1202)( 607 1214)( 613 1226)( 617 1234)( 619 1238)
( 631 1262)( 641 1282)( 643 1286)( 647 1294)( 653 1306)( 659 1318)
( 661 1322)( 673 1346)( 677 1354)( 683 1366)( 691 1382)( 701 1402)
( 709 1418)( 719 1438)( 727 1454)( 733 1466)( 739 1478)( 743 1486)
( 751 1502)( 757 1514)( 761 1522)( 769 1538)( 773 1546)( 787 1574)
( 797 1594)( 809 1618)( 811 1622)( 821 1642)( 823 1646)( 827 1654)
( 829 1658)( 839 1678)( 853 1706)( 857 1714)( 859 1718)( 863 1726)
( 877 1754)( 881 1762)( 883 1766)( 887 1774)( 907 1814)( 911 1822)
( 919 1838)( 929 1858)( 937 1874)( 941 1882)( 947 1894)( 953 1906)
( 967 1934)( 971 1942)( 977 1954)( 983 1966)( 991 1982)( 997 1994)
Of course as Cory pointed out, you could see that a number smaller than 1000 must necessarily have its multiples repeat at an interval smaller than 1000, and necessarily have a member fall into {1001,...,2001}.
  Posted by Charlie on 2003-03-08 09:40:31

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