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73 arithmetic/digits/prime/change.one.p




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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

73 arithmetic/digits/prime/change.one.p


What is the smallest number that cannot be made prime by changing a single
digit? Are there infinitely many such numbers?

arithmetic/digits/prime/change.one.s

200. Obviously, you would have to change the last digit, but 201, 203,
207, and 209 are all composite. For any smaller number, you can change
the last digit, and get
2,11,23,31,41,53,61,71,83,97,101,113,127,131,149,151,163,173,181, or 191.

200+2310n gives an infinite family, because changing the last
digit to 1 or 7 gives a number divisible by 3; to 3, a number divisible
by 7; to 9, a number divisible by 11.

 

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