Why 30 is the largest integer such that none of its ?

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SUMMARY

The largest integer such that none of its totatives are composite is 30. This is established by identifying that all coprime numbers below 30—specifically 7, 11, 13, 17, 19, 23, and 29—are prime. The integer 30 can be factored into its prime components as 2, 3, and 5, which confirms its status. In contrast, integers like 60 and 210 do not meet this criterion due to the presence of composite totatives.

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Why 30 is the largest integer such that none of its...?

Why 30 is the largest integer such that none of its totatives are composite?
which means All the coprime numbers that below 30 are primes..
30=> 7,11,13,17,19,23,29
?//
and if you have a proof that it is the biggest integer please Help me...
 
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HussamLawen said:
Why 30 is the largest integer such that none of its totatives are composite?
which means All the coprime numbers that below 30 are primes..
30=> 7,11,13,17,19,23,29
?//
and if you have a proof that it is the biggest integer please Help me...

Hi HussamLawen! Welcome to PF! :smile:

Hint: 30 = 2.3.5 …

60 doesn't work because … ? :wink:
 


tiny-tim said:
Hint: 30 = 2.3.5 …

60 doesn't work because … ? :wink:

And 210 doesn't work because... ?
 

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