Is 1 a Prime Number?

A prime number is any integer number that is divisible only by 1 and itself. 1 certainly satisfies this definition. However, there is a convention to exclude 1 from the set of the primes to make formulations of some theorems simpler.

For instance, if to treat 1 as a prime, then the theorem about uniqueness of factorization of any integer into a product of degrees of primes is incorrect since 1 can be included with any degree, which makes factorization non-unique. To save a beautiful and useful result, one either has to provide a lengthy additional explanation (like a clarification that uniqueness holds only if the possibility of including 1 in any whole degree is ignored) or merely to agree not to count 1 as a prime. Long ago mathematicians agreed to stick to the latter.

No

No. A prime number is divisible by exactly two distinct natural numbers, 1 and itself.

no, but that's your rank and IQ!

no. The first one is 2, then 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

according to mathematical concepts, A NUMBER DIVISIBLE BY ITSELF AND ALSO ONE, is a prime number. so, 1 satisfies this condition and so it is a prime number.
BUT, 5*1=5, 5*1*1*1....=5,.....
the use of one in division or multiplication is really ambiguous. but prime number is a basic number, also the use of one in multiplication and division is unnecessary.
hence, 1 CANNOT BE CONSIDERED AS A PRIME NUMBER!

No. 1 is a "unit" and "units" are excluded from being primes.

If you include negative numbers too, then -1 is a unit and factorizations are unique except that any of the primes may be multiplied by a unit. So 3*7 and -3*-7 count as the same factorization.

A primenumber is number which can only be divided by itself and 1. Therefore,1 is a primenumber,because 1 applies to the defintion of a primenumber.

I believe that a primenumber is a number which is only divisible by itself and 1. I can't understand why 1 isn't a primenumber.Because 1 applies to those demands.Or am I wrong?

This question has been asked a few days ago and I explained why mathematicians decided not to treat 1 as a prime number. Doing so would make formulations a some theorems bulky and cumbersome. For instance, factorization into primes would not be unique so a long explanation of the exception would be necessary to save this truly useful feature. So, it's a matter of convenience -- pretty common in math.

"A prime number is divisible by exactly two distinct natural numbers, 1 and itself."

1 is divisible by 1 and 1 (itself), but these 2 divisors are not distinct natural numbers, therefore by definition 1 is not a prime number.