The sum of two prime numbers is 999. Write these two prime numbers

The sum of two prime numbers is 999. Write these two prime numbers

These two prime numbers are 2 and 997

p. If q is prime and 5p + 7q = 29, then p + q =?
We need to make clear the reasons,
Need specific reasons

p=3,q=2
p+q=5

If M = P4 (p2q + 1), where P and Q are prime numbers and Q-P = 29, then M = ()
A. 2009B. 2005C. 2003D. 2000

The value of M should be innumerable from small to large. Due to the limited options, it is impossible to be very large. The difference between P and Q prime numbers is 29, and ∵ even prime number is only 2. When p = 2 and q = 31, M = P4 (p2q + 1) = 2000 is the required value. Therefore, D

We know that M = P ^ 4 * (P ^ 2 * q + 1), where P and Q are prime numbers, and Q-P = 29, which satisfies the value of M
It is known that M = the fourth power of P * (the square of P * q + 1), where P and Q are prime numbers and Q-P = 29, satisfying the value of M

p. Q is prime and Q-P = 29
∴p=2,q=31
M=P^4*(P^2*q+1)=2^4(2^2*31+1)=4000