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When p is a prime number, 17p + 1 is a square number
17p + 1 = R ^ 2, 17p = R ^ 2-1 = (R + 1) (R-1), so R + 1 = 17 or R-1 = 17, if R + 1 = 17, r = 16, R-1 = 15, it is not prime, if R-1 = 17, r = 18, R + 1 = 19 = P, so p = 19,
17p + 1 is a square number
P is prime, the square of P + 2 is also prime, what is the value of P, how to find it, please prove
P = 3K + 1 K is a positive integer
P ^ 2 + 2 = 9K ^ 2 + 6K + 3 = 3 (3K ^ 2 + 2K + 1) the factor 3 is not prime
p=3k-1
P ^ 2 + 2 = 9K ^ 2-6k + 3 = 3 (3K ^ 2-2k + 1) with factor 3 is not prime
So p can only be a multiple of 3, P = 3
What is the product of two prime numbers?
The product of two prime numbers must be a composite number
Because a composite number has a factor other than 1, then these two prime numbers are the factors of the composite number
The sum of two prime numbers is 18 and the product is 77. These two numbers are______ And______ ．
77 = 11 × 7, 11 + 7 = 18, so the two numbers are 11,7
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