Four wrongs don't make a right

Algebra Level 2

A chemist, a physicist, an engineer and a theologician were asked to determine how many odd prime numbers there are less than 50. They knew that 1 was not to be considered a prime.

CHEMIST: 3, 5 and 7 are prime. That's enough evidence to conclude that all the odd numbers (other than 1) less than 50 are prime. So the answer is 24.

PHYSICIST: 3, 5, 7, 11 and 13 are prime. 9 must be an experimental error. I therefore conclude that all odd numbers other than 1 are prime. So the answer is 24.

ENGINEER: I'll test them all. 3 is odd and prime... 5 is odd and prime... 7 is odd and prime...9 is odd and prime... ...49 is odd and prime. That means there are 24 such numbers.

THEOLOGICIAN: 3 is odd and prime, therefore I will take it on faith at all odd numbers greater than 1 are prime. So the answer is 24.

How many odd prime numbers are there less than 50? (It's not 24.)


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