Mark all true statements.
Group of answer choices
It is possible for a positive integer to have two prime factorizations such that the prime factor 3 appears in one of them but not the other.
A prime number is a positive integer that is only divisible by 1 and itself.
The sum of two primes is prime.
If p and q are distinct primes, then they are also relatively prime to each other.
To test whether 101 is prime, you only need to divide it by 2,3,5 and 7. If it is not divisible by any of those numbers, then it is prime.
If there are only finitely many primes, then 1=2.
The number n can have at most the floor of base-2 log of n many prime factors, if prime factors are counted with repetition (i.e. 2*3*3*5 has 4 prime factors.)
If p is prime and n is a positive integer, then the number pⁿ has exactly n positive divisors.
The sequence of prime numbers follows no exact pattern.
If p and q are primes, then pq+1 is also prime.
The number of prime numbers between 1 and 100 is greater than the number of prime numbers between 1000 and 1100.
If the positive integers a and b are relatively prime, then so are a+1 and b+1.
If p is prime, then p+2 may or may not be prime, i.e. there exist primes p such that p+2 is prime, and there exist primes p such that p+2 is not prime.
There is a largest prime, and it is about the size of Graham's number.