When a prime is divided by 60, the remainder is a composite number. When a second prime is divided by 60, the remainder is a prime. Find the smallest possible value of the second prime.

MEMEG0D Oct 30, 2024

#2**+1 **

*When a prime is divided by 60, the remainder is a composite number. When a second prime is divided by 60, the remainder is a prime. Find the smallest possible value of the second prime.*

2 is the smallest prime. 2 / 60 = 0 R 2 so the remainder is a prime as well.

However, I think that is not the intent of the problem. Let's go larger than 60.

Note the smallest primes – 2, 3, 5, 7, 11, etc – and then add to 60

62 not prime

63 not prime

65 not prime

**67** prime and 67 / 60 = 1 R 7 and the remainder is prime as well.

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Bosco Oct 30, 2024