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unprimeable numbers
A composite number is called unprimeable if it cannot be turned into a prime by changing a single digit.

For example, 144 is not unprimeable, because changing the last digit into a nine we obtain 149, a prime. The number 200 is instead unprimeable (the smallest one), since none of the numbers 201, 203, 207, 205, and 209 are prime and all the other numbers which can be obtained from 200 (say, 300, or 270, or 208) are even, so they are not prime.

It is easy to prove that unprimeable numbers are infinite, since, for example, all the numbers of the form are unprimeable.

A prime which cannot be turned into another prime by changing a single digit is called weakly prime.

Up to there are 2855169 unprimeable numbers.

The smallest unprimeable numbers ending in 1, 3, 7 and 9 are, 595631, 1203623, 872897, and 212159, respectively.

The first unprimeable numbers are 200, 204, 206, 208, 320, 322, 324, 325, 326, 328, 510, 512, 514, 515, 516, 518, 530, 532, 534 more terms

Unprimeable numbers can also be... (you may click on names or numbers and on + to get more values)