It is well known the the gap between two consecutive primes can become arbitary large.
Is this also the case with the totient numbers and the even nontotient numbers ?
The fist record differences for the totient numbers are :
[12, 16, 4]
[72, 78, 6]
[240, 250, 10]
[864, 876, 12]
[4032, 4048, 16]
[10566, 10584, 18]
[14260, 14280, 20]
[35170, 35192, 22]
[64520, 64544, 24]
[112690, 112716, 26]
[134640, 134668, 28]
[159120, 159152, 32]
[597080, 597116, 36]
[1039680, 1039720, 40]
[2307316, 2307360, 44]
[5313462, 5313512, 50]
[9377212, 9377272, 60]
[114748704, 114748768, 64]
[186694480, 186694552, 72]
Can the difference be arbitary large ?
In the case of the non-totient numbers, to get a large difference, we must omit the odd numbers which are non-totient except $1$. The first two even non-totient numbers are $14$ and $26$ with diferrence $12$. Upto $10^7$, the only differences greater $12$ occuring are
[98, 114, 16]
[496, 510, 14]
[267668, 267682, 14]
Is $16$ the maximum possible gap ?