Yes, in fact, there is no last Prime number - the set of prime numbers is infinite. The proof was already known 2000 years ago:
If you assume that there is a last prime number, multiply all prime numbers up to that "last prime number". Then add one. The result is either a prime number itself, or it is composed of factors, none of which is one of the prime numbers you multiplied (because of the added 1). Thus, the original assumption (that there is a last prime number) has to be false.
Example: The first 3 prime numbers are 2, 3, 5. If you multiply them, you get 30. Add one to the result, and you get 31. This number isn't divisible by 2, by 3, nor by 5. It happens to be a prime, but this isn't always so.
Mutliplied two prime numbers to get 400?
No.
There is only one number that equals 400. The number is 400, and it's not a prime number.
The prime factors are: 2, 5
I'm sure there are more than 2 prime numbers that are 400 digits long.
You will need to multiply six prime numbers to obtain 400: 400 = 5*5*2*2*2*2
The sum of all prime between numbers 1 and 400 (2 through 399) is 13,887.
There are no two prime numbers that would generate 400. The prime factorization of 400 is 2^4 * 5^2, which means it can be expressed as the product of two powers of primes, but not as the product of two distinct prime numbers.
307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397
400 to 500
The happy prime numbers between 300 and 400 are as follows:313, 331, 367, 379, 383, 397
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113, 127,137,139,149,151,157,163,167,173,179,181,191,193,197,199.