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Q: Can a prime number ever have composite factors?

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A prime number has exactly two factors, 1 and the number itself. 1 is not a prime number, and the product will be a composite number if any other prime is used as a factor and multiplied by another prime.

All of them except 97 which is a prime number

There are no two "last" composite numbers. Just as with prime numbers, and all numbers, they go on for ever and ever and ever and ever ... ... .

Prime numbers can ONLY be divided (without a remainder) by themselves and the number 1. No even number can ever be a prime number. The number 10 is an even number and can be divided by 5 (10/5=2) and 2 (10/2=5)

No.

Yes.

Absolutely !.. Any prime number only has itself and 1 as its factors.

No one has ever discovered the mathematical pattern for prime numbers and all that is known about them is that each prime number has only 2 factors which are itself and one.

No.

It has not, will not and cannot be found.

That statement is false. For example, the number 900, which equals 30 squared, has the prime factors 2, 3 and 5. But many other non-prime factors exist for it such as 9, 15, 50, 100, 300 and 450. A square can be constructed with any number of prime factors, too. For example, here is one with 4 prime factors: 22 * 32 *52 * 72 = (2*3*5*7)2 = 2102 = 44100.

No.

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