Prove that if p1 p2 and pn are distinct prime numbers wi

Prove that if p1, p2, . . . , and pn are distinct prime numbers withp1 =2 andn >1,then p1p2···pn +1 can be written in the form 4k + 3 for some integer k

Solution

let us list some prime numbers,

2,3,5,7,11,13,17,19,23,29,31,37....

first property, it will be odd

so if the prime numbers are distinct then, of course for different values of k they can be written in the form 4k+3, but some of the numbers will not be included in those like 5,13,17,29 etc