Re: Prime Number Progressions
- Hi and welcome to the list! Yes certainly this is the place to share
your findings, certainly myself and others would be interested in
seeing your work and the kind of progressions you are talking of.
From the Prime Pages, here's a progression that Euler came up with
over 200 years ago:
41, add 2 = 43
43, add 4 = 47
47, add 6 = 53
53, add 8 = 61
61, add 10 = 71
71, add 12 = 83
and so on for 33 more terms to yield 40 primes! All of which is the
same as the equation
x^2 + x + 41 for x=0 to x=39.
In 1998 Manfred Toplic found ten consecutive primes in arithmetic
P = 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004
18036 03417 75890 43417 03348 88215 90672 29719,
+210, + 420, + 630, + 840, + 1050, + 1260, + 1470, + 1680 and + 1890.
I wouldn't doubt if others have found larger by now. I think it was
Phil Carmody who came up with a big one fairly recently but I don't
know how big.
--- In firstname.lastname@example.org, ginnyw@a... wrote:
> I am new to the list and would like to know if others are
> finding progressions of prime numbers. I have written a program
which searches for
> the progressions. While the results aren't spectacular, the number
> progressions found is perhaps new. For example the program found
54 progressions of
> 11 primes, 2 progressions of 18 primes, etc. Is this a subject for
> and if it is, would someone be interested in reviewing my work.
> Thank you.
> Virginia W.
> [Non-text portions of this message have been removed]
Thank you for your email. The progressions are the ordinary arithmetic type.
One of the progressions of 11 primes is:
17 add 44 = 61
61 add 88 = 149
149 add 132 = 281
281 add 176 = 457 and continuing for 6 more terms until a nonprime 2921 is
My program uses a constant to search for the progressions. I started with
pencil and paper and then wrote the program. Except for the progression which
generates 40 primes, the largest progression I have to date generates 29
primes. Perhaps that might be a record. Most of the progressions are with small
numbers because of the limitations of my computer.
[Non-text portions of this message have been removed]