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It is known that the set of two-prime-digit prime integers is { 23 , 37 , 53 , 73 } \{23,37,53,73\} .

If we put 3 3 in the leftmost position of each integer, then we have { 323 , 337 , 353 , 373 } \{323,337,353,373\} , which are all prime integers.

If we do the same from these three-digit numbers to get { 3323 , 3337 , 3353 , 3373 } \{3323, 3337, 3353, 3373\} , are these four-digit integers all prime?

Yes, it is possible No, it is not possible

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2 solutions

Edwin Gray
Aug 29, 2018

3337 = 59^2 - 12^2 = 47*71, so composite. Ed Gray

Vijay Simha
Dec 2, 2017

It can be seen that 3337 has divisors other than 1 and itself. 3337 can be divided by 47 and 71.

3353 has divisors other than 1 and itself. 3353 can be divided by 7 and 479

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