However, at first sight the generalisation looks to be correct But, eventually it was
shown that
225
1
+  = 232 + 1 = 4294967297
which is not a prime since 4294967297  =  641 × 6700417 (a product of two numbers) So the generalisation “For each n, 
22
1
n +  is a prime (n ∈ N)” is false Just this one example 
225
1
+  is sufficient to disprove the generalisation