Does a prime number multiplied by a prime number ever result in a prime - Why? Does a nonprime multiplied by a nonprime ever result in a prime - why? Is it possible for an extremely large prime to be expressed as a large integer raised to a very large power? Explain. Are there infinitely many natural numbers that are not pri

If R is a unique factorization domain and if a and b in R are relatively prime
(i.e.,(a,b) = 1), whenever a divides bc, then a divides c.
That is, if R is a unique factorization domain and if a and b in R are relatively prime
(i.e., (a,b) = 1), whenever a divides bc then a divides c.

Let phi:R->S be a homomorphism of commutative rings
a) Prove that if P is a prime ideal of S then either phi^-1(P)=R or phi^-1(P) is a prime ideal of R. Apply this to the special case when R is a subring of S and phi is the inclusion homomorphism to deduce that if P is a prime ideal of S then PR is either R or prime ideal in

Wholesale company produces circuit breaker containers. The machine operator stamps 15 containers from each strip of aluminum. Each strip costs $1.15. The operator can stamp 540 containers per hour. The direct labor charge is $17.85 per hour. What is the prime cost of manufacturing a circuit breaker container?
a.$.32 b.$.03 c

Please help with the following problem.
Write a program that computes and prints the 1000th prime number using code blocks c++.
a. You will need some variables to keep track of which prime number you're on and keep track of where you are in your loop.
b. Need to test odd numbers to see if they are prime..
c. Need two l

For this problem it helps to know that: 3x7x13 = 273
(a) Define the Euler Totient function, (SYMBOL)
For (b) to (f) please see attached.
(PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM AND PROPER SYMBOLS)