No it is not, you can test this by trying to divide 781 by all prime numbers (p)
where p^2<=781.
note that 11 divides 781 evenly, with a remainder of 71.
11 is prime, and the existing factors of 71 can be tested using the same method, p^2<=71.
noting that 9^2>71, we know if 71 is not prime, a prime number less than 9 must divide it.
and since 2, 3, 5, and 7 do not divide 71 that is also prime
Thus 781 is not prime, and the factors of 781 are 11 and 71.
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A prime number times a prime number is a composite number. Since prime numbers, except for 2, are odd numbers, a prime number times a prime number is usually an odd number. It will only be an even number if one of the prime numbers is 2. A prime number times a prime number will be a number with four factors unless both prime numbers are the same, in which case it will be a square number with only three factors.
101 is a prime number. The only factor of 101 is itself and 1.prime