Unique Groupings found in the first 49 mersenne numbers

[George M]

Say we take a number 15. This is equal to 3 x 5. Because it is divisible by 3, then the numerology of this product, namely 15, will also add to a number that is divisible by 3. Since every prime number (apart from 3) is not divisible by 3, then the digits will simply not add to 6, 9, 12, 15, 18, 21, 24, ... etc. This is called the “Divisibility by 3 Rule”, and as a numerologist I believe you should know about this.

I am passionate in numerology as well and have made a conjecture on the numerology of A^2 - B^2 for integers A and B. The only constraint is that if B = 0, then A is equivalent to 2, 4, 7 (mod 9). This conjecture also involves squared numbers, and particular cycles which I call “orbits”. I was able to prove this was true for B = 0, but not for the rest of the integers. If you are interested, you can private message me and I will send it to you :)

[ONeil]

Originally Posted by gophne

Hi ONeil

Interesting. Off course 3, 6 & 9 won't appear because if the addition of the digits would have 3, 6 or 9 as a sum, they would be divisible by 3.

What is very interesting, but still probably not a pattern, is how many times in the list a particular sum of the digits repeats itself!

How on earth did you manage to find the sum of the digits of the higher mersenne prime numbers?

I actually summed the P that is associated with the mersenne Prime to a numerology number. I would really like to add up the mersenne primes to a numerology number and see what they become as a numerology number but that might be to cumbersome

[Batalov]

Originally Posted by ONeil

I would really like to add up the mersenne primes to a numerology number and see what they become as a numerology number but that might be to cumbersome

We can help you out. You don't have to sum up digits. Here, ironically, for decimal expansions of Mersenne primes, you are not saving time by writing the number and then summing up digits - instead you are wasting it. Tons of time wasted - writing out twenty million digit numbers and summing their digits up.

Instead, what you apparently want to do it to compute Mod(2,9)^p-1. That is almost instantaneous already, but you can do even better by doing math. Math will tell you that Mod(2,9)^p-1 is a periodic function and repeats over every 6 values:

p%6             0    1    2    3    4    5
Mod(2,9)^p-1    0    1    3    7    6    4

You can set aside p=2 and 3 as special cases, while all the rest will be either 1 or 5 mod 6.

So, for p>=5, if p%6 == 1 then your digital root of the Mersenne prime will be 1, else it will be 4. The end.

[gophne]

Originally Posted by ONeil

I actually summed the P that is associated with the mersenne Prime to a numerology number. I would really like to add up the mersenne primes to a numerology number and see what they become as a numerology number but that might be to cumbersome

Hi ONeil

Oh, I thought you had summed up the digits of the mersenne primes themselves, but still interesting. As stated elsewhere numerology is a popular approach to find a pattern to any regular series, e.g 2,3,4,5,6,7,8.9 times tables, with interesting answers w.r.t the cycles of these, base 10.

You might want to refer to Batalov post #22. In it he suggests that it might be easy to do the sum of the digits of the value of the mersenne numbers as well. MIGHT make for interesting results.

I think that there might either be programme code in some software packages to do this, or the code gurus would know how to programme for this.

[gophne]

Originally Posted by Batalov

He didn't.
(Even though it is elementary.)

Hi Batalov

I have to hand it to you.... x mod 9 does return the sum of the digits of any number...amazing.

I did not know this because I don't work with modulo function on a regular basis, except for narrow purposes of finding answers to specific modulo equations...has cost me dearly.

I have spent hour upon hours adding digits of numbers in the past, often getting incorrect answers as you could imagine, not knowing x mod 9 delivered the answer instantaneously!

Respect...aka Ali-G

[GP2]

Originally Posted by Batalov

He didn't.
(Even though it is elementary.)

Originally Posted by gophne

Oh, I thought you had summed up the digits of the mersenne primes themselves

In case anyone is actually interested in the digit sum itself (as opposed to the "recursive digit sum", i.e., digital root), there's an OEIS sequence for everything.