The Eleven-and-Higher Matrix of Primes and non-primes

original to FR | July 16, 2025 | Peter O'Donnell

[Red Badger]

The number of respondents to this post will be a prime number................

[rlmorel]

I find Prime Numbers interesting (in much the same way I find Pi interesting) but not really enough for me to ask any questions...

But I do know we have a number of math geeks here on FR, so you should have company shortly!

[spokeshave]

But is there a signal on the sub-harmonic ..Kenneth needs to know.

[\/\/ayne]

I fed it to Grok 3

[E. Pluribus Unum]

I have played around with prime numbers and formed the hypothesis that almost all prime numbers end in 3, 7 or 9. Not sure if it’s true.

[Rio]

It’s good to have a hobby.

[ComputerGuy]

What is the true meaning of Pi?

[Repeal The 17th]

“...a multiple of 5, because it will end with 5...”
-
Or zero.

[1Old Pro]

the ratio of a circle’s circumference to its diameter.

[sonova]

“...a multiple of 5, because it will end with 5...”
-
Or zero.

+++++++++++++++++++++++

I almost replied similarly, but the author is talking about odd multiples of 5...(I think)

[Peter ODonnell]

I think there are equal numbers of primes ending in 1, 3, 7 and 9. There are only two exceptions, 2 and 5. The 48 row entries in two columns have equal numbers ending in 1, 3, 7 and 9; assuming that capture is equally distributed, that would knock out equal proportions in each row (which looks to be very close to being the case, it is probably fractionally different at any moment in time moving across the grid).

Note to all readers: Error in original post, first number in column 201 is 21001 (not 20101 as I typed). Wish we had an edit function. I know cowboyusa could use one.

[Governor Dinwiddie]

One of the more interesting books on prime numbers and the zeta function is John Derbyshire's "Prime Obsession". It's written for the popular audience, and it's quite a good read.

Some might remember John from his stint at the National Review, which fired him for speaking the truth. From the Wikipedia article:

Derbyshire suggested that white and East Asian parents should talk to their children about the threats posed to their safety by black people. He also recommended that parents tell their children not to live in predominantly black communities. He included the line "If planning a trip to a beach or amusement park at some date, find out whether it is likely to be swamped with blacks on that date."

Very sensible advice.

[algore]

2^136,279,841 - 1

[metmom]

Well, I was following until we got about 1/4 the way in.

After which, my kids, who are math nerds would ting interest in this exercise.

It’s beyond me.

[\/\/ayne]

Whoops I deleted it so here's Grok3 take on it again.

[bwest]

Interesting post. I suggest you read about the Sieve of Eratosthenes.
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

[Steely Tom]

But it occurred to me that if you could predict non-primes (basically the odd numbers that are not primes) then that would be equivalent to predicting primes. An odd number is either prime or non-prime.

"Predicting non-primes" and then eliminating them is what happens in the ancient algorithm called the Sieve of Eratosthenes.

[Steely Tom]

Interesting post. I suggest you read about the Sieve of Eratosthenes.

Oh darn!

[ladyrustic]

Thanks for posting.

I’ve been fascinated by prime numbers too, although I must admit it’s been at least 3 years since I was last thinking about them and possible ways to identify new primes quickly. I’m glad I’m not the only weirdo who loves primes. I’m convinced God gave us prime numbers for the great pleasure found in the challenge they pose. Your post had me digging through some of my old programs to refresh my memory on what I was striving for with them back in the day:

In those old (and sadly incomplete) musings, I was trying to develop more of an architectural solution, a way of pinpointing the location of primes in arrays without having to do any cumbersome numerical calculations, the goal being to quickly know their “geographical position” without the absolute necessity to calculate value unless needed.

Sadly I’m too old now to be intellectually helpful on the subject, as I just cant think deeply enough anymore, but its still all very much a fun mystery, and I’d enjoy perusing whatever thoughts you and others might have on the subject.