Four wrongs don't make a right
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.)
The answer is 14.
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1 solution
Using the Sieve of Eratosthenes, we quickly list the odd primes less than 50 as 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
Counting them, we find 14 odd primes.