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Never prime! (2) (Posted on 2010-09-04) Difficulty: 2 of 5
The value of the smallest positive base ten integer that cannot be changed into a prime by changing a single digit was determined in Never prime!.

Determine the respective minimum values of a positive base N integer P that cannot be changed into a prime by changing a single digit, whenever N is a positive integer with 3 ≤ N ≤ 16, but N ≠ 10.

Note: P cannot contain any leading zero, and the first digit of P (reading left to right) cannot be changed to a zero.

No Solution Yet Submitted by K Sengupta    
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solution | Comment 2 of 4 |
I'm a bit unsure as to whether or not our value P can be a prime itself, so I'll give the primes-acceptable solution, with the variants in parentheses if they are necessary. The second value(s) are the number P converted into the appropriate base.

Base 3; P = 7 (24); 21 (220)
Base 4; P = 24; 120
Base 5; P = 67 (90); 232 (330)
Base 6; P = 90; 230
Base 7; P = 119; 230
Base 8; P = 200; 310
Base 9; P = 117; 140
Base 11; P = 319; 270
Base 12; P = 528; 380
Base 13; P = 1131; 690
Base 14; P = 1134; 5B0
Base 15; P = 525; 250
Base 16; P = 1328; 530

EDIT: Thanks Charlie, I was a little tired when I was typing those in, and for 3 and 4, converted them on my own. Wasn't thinking straight, and just did 24/4 = 6.

Edited on September 5, 2010, 4:58 pm
  Posted by Justin on 2010-09-04 19:44:21

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