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