000RM.dvi

626 Strings of composites

Project: Strings of consecutive composite values ofn^2 +n+1

Find the first strings of consecutive composite values ofn^2 +n+1.

mn···n+m− 1

39 ··· 11

528 ··· 32

Project

The first string of 99 consecutive composite values ofn^2 +1begins with
n= 45371. The string with more than 100 composite values ofn^2 +1
has 111 members beginning with 82735. What is the longest of such a
string you can find?