Sandy claims that 50!+31 is a prime number because none of the divisibility tests work and to her it looks prime. Sandy is wrong. Explain why 50!+31 is not prime and why her explanation is wrong

Question

anonymous · Answer

prime number should be the one (50! + 3!) + 1

anonymous · Answer

no..
it goes like this...

anonymous · Answer

$$50!=50\times49\times48\times\ldots\times32\times31\times30\times\ldots\times2\times1$$
so, 31 is a factor of 50!
so, let $50! = 31\times c$
$$(50!+31)=(31\times c+31)=31(c+1)$$
this number is clearly divisible by 31
and hence not a prime

anonymous · Answer

Inkyvoyd, I have some additional questions. Think you could help me out?