21.3 F ̈urstenberg’s topological proof made easy 607
Exercise
1.Letpndenote then-th prime number. Find the smallest value ofn
for whichp 1 p 2 ···pn+1is not a prime number.2.Find the smallest value ofnfor whichp 1 p 2 ···pn− 1 is not a prime
number.3.Find the smallest value ofn> 3 for whichn!+1is a prime number.4.Find the smallest value ofn> 7 for whichn!− 1 is a prime number.5.Find a shortest sequence of prime numbersp 1 <p 2 <···<pn
satisfying the following conditions.
(i)p 1 =2,
(ii)pk+1< 2 pkfork=1, ...,n− 1 ,
(iii)pn> 10000.