9737333

9737333 is a primer number. It’s the 648391th primer number actually. But 648391 is a prime number too! It is the 52711th primer number, what a coincidence. Guess what… yes, 52711 is a primer number as well, it’s the 5381th primer number. I don’t need to tell you 5381 is prime, although I will tell you it is the 709th one, and that 709 is the 127th one. Mr Mersenne new 127 is the 31th prime number, and we all know 31 is the 11th primer, that 11 is the 5th, that 5 is the 3rd, that 3 is the second, and that 2, and not 1, is the first primer number.

I wrote after a bit of playing one day that I realized that 17 is the 7th primer number and that 7 is a prime itself, which is cool. I decided to study this, and produced the following sequences:

2 3 5 11 31 127 709 5381 52711 648391 9737333 …
7 17 59 277 1787 15299 167449 2269733 …
13 41 179 1063 8527 87803 1128889 …
19 67 331 2221 19577 219613 3042161 …
23 83 431 3001 27457 318211 4535189 …
29 109 599 4397 42043 506683 7474967 …
37 157 919 7193 72727 919913 …

I though I was going to study this a little bit more, only to do a search in oeis.org and discover that, of course, somebody studied this things before me a few years ago. Sight.

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