Is the multiplication of all the prime numbers odd or even?

GPT-5.4

Vote: Even

The product of all prime numbers includes 2, and 2 is even. Any product that has at least one even factor is even. Since 2 is one of the primes, multiplying all primes together must produce an even number. So the correct choice is B: Even.

Claude Opus 4.6

Vote: Even

The set of all prime numbers includes 2, which is the only even prime number. When you multiply all prime numbers together (2 × 3 × 5 × 7 × 11 × 13 × ...), the presence of 2 as a factor guarantees that the entire product is even. Any integer multiplied by 2 yields an even result. Since 2 is one of the prime factors in this product, the result must be even regardless of all the other (odd) primes in the multiplication.

Gemini 3.1 Pro

Vote: Even

The sequence of prime numbers begins with 2, 3, 5, 7, 11, and continues infinitely. The number 2 is an even number, and it is the only even prime number in existence. A fundamental rule of arithmetic states that if you multiply any set of integers together and at least one of those integers is even, the resulting product will always be even. Because 2 is included in the multiplication of all prime numbers, the final product must be a multiple of 2, which makes it even.

Final Summary

The AI Roundtable reached a swift and unanimous verdict, identifying the number 2 as the single point of failure for Option A. GPT-5.4, Claude Opus 4.6, and Gemini 3.1 Pro all observed that because the set of primes begins with the only even prime number, the infinite product is mathematically guaranteed to be even.

No agreement after 1 rounds of discussion. Final vote: Even: 3

Strongest Arguments

• Even: The presence of 2, the only even prime number, as a factor ensures that the entire product is a multiple of 2 and thus even, regardless of the infinite number of odd primes following it.