Number Theory Problem of the day 11-17

[Steven G]

Show that given any n>0 we can find n consecutive composite integers.

 

[blamocur]

Spoiler

[imath][n!, n!+n][/imath]

 

[blamocur]

Actually,

Spoiler

[imath][(n+1)!+2, (n+1)!+n+1][/imath]

 

[blamocur]

Actually,

Spoiler

[imath][(n+1)!+2, (n+1)!+n+1][/imath]

Number theory can be entertaining with some minimal coding skills. For example, all 113 numbers between primes 492113 and 492227 are composite, but the above formula would find such stretch only after [imath]114![/imath], which is greater than [imath]10^{186}[/imath]

 

[Steven G]

Number theory can be entertaining with some minimal coding skills. For example, all 113 numbers between primes 492113 and 492227 are composite, but the above formula would find such stretch only after [imath]114![/imath], which is greater than [imath]10^{186}[/imath]

Number Theory is extremely interesting. I am enjoying studying this subject.