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Not necessarily. 71 is a Prime number, 7 is a prime number, and 71-7= 64, which is NOT a prime number.

In most cases, the difference of two prime numbers will not be a prime number. All prime numbers greater than 2 will be odd numbers. The difference between two odd numbers will be an even number. Unless that even number is 2, it is not a prime number. Here are some additional examples:

19, 13: difference 6, not prime

23, 7: difference 16, not prime

53, 31: difference 22, not prime

61, 59: difference 2, prime

113, 109: difference 4, not prime

293, 283: difference 10, not prime

331, 101: difference 230, not prime

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Q: Is the difference of two prime numbers a prime number?
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