TITLE: Gap between composite numbers that aren't divisible by 2,3 or 5
QUESTION [6 upvotes]: It is easy to determine if a number is divisible by 2,3 or 5, so in my experiment i am concentrating on a consecutive list of composite numbers that are not divisible by 2,3 or 5.
My question is if there is a maximum gap limit between such numbers, and if so what is it?
Please review the image as an example:

REPLY [4 votes]: These numbers are prime
1418575498609,  1418575498607,  1418575498603,  1418575498601,  1418575498597,  1418575498591,  1418575498589,  1418575498583,  1418575498579,  1418575498577,  1418575498573
which gives a gap of 42 between 1418575498571 and 1418575498613
They are 614101948*2310 - 1260 -[11,13,17,19,23,29,31,37,41,43,47]
Edit
Suppose we look at numbers near $N$, which might be $10^{13}$.
The chance a number $x$ is prime is $1/\ln(N)$.  Prime factors up to 11 are ruled out by the 2310 formula, so the chance of being prime is increased to
$$P=\frac{\frac21\frac32\frac54\frac76\frac{11}{10}}{\ln N}$$
The chance all eleven numbers are prime is $P^{11}$.
The 2310 formula gives two opportunities every 2310, namely $2310k+1260+[11,...]$ and $2310k-1260-[11,...]$
So an estimate for the number of solutions within $N/2$ of $N$, so between $N/2$ and $3N/2$, is
$$\frac{P^{11}N}{1155}$$
That suggests about 4 near $N=10^{12}$, but I have only found one.