The number of prime numbers among the numbers 105! +2 ,105! +3, 105!+4......105!+104 , 105!+105 is ??

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Answer 1 · 2017-10-25T12:14:59

There are no prime numbers here.

Every number in the set is divisible by the number added to the factorial, so it is not prime.

Examples

#105!+2=2xx3xx4xx...xx105+2=#
#=2xx(1+3xx4xx...xx105)#

It is an even number, so it is not prime.

#105!+101=2xx3xx...xx101xx...xx105+101=#
#(2xx3xx...100xx102xx103xx104xx105+1)xx101#

This number is divisinble by #101#, so it is not prime.

All other numbers from this set can be expressed in this way, so they are not prime.