A primorial-based place value number system


Here’s something I’ve been working on in my head for a bit, that I couldn’t quite work out but think I’ve finally managed to get. I think this is going to help me work through some of my current roadblocks, since I believe the complete set of prime numbers is fully symmetric within primorials.

Consider a number of the form:

.., ZZZ, …, D,C,B,A (as necessary)

Where A can be 0 or 1 (2 possible values), and each A has a value that is a corresponding multiple of 1, or P0#;

B can be 0, 1 or 2 (3 possible values), each having a value corresponding to a multiple of 2, or P1#;

C can be 0, 1, 2, 3 or 4 (5 possible values), each multiplied by 6, or P2#;

H can be 0, 1, 2, … or 18 (19 possible values), each multiplied by 30030, or P7#

… and so on.

Some examples:

5,2,2,1 = 167 = (1 + 2 x 2 + 2 x 6 + 5 x 30)

2,1,1,1,1,2,1,0 = 1053614 = (0 x 1 + 1 x 2 + 2 x 6 + 1 x 30 + 1 x 210 + 1 x 2310 + 1 x 30030 + 2 x 510510)

1,15,0,0,0,0,0,1 = 960961 = (1 x 1 + 0 x 2 + 0 x 6 + 0 x 30 + 0 x 210 + 0 x 2310 + 15 x 30030 + 1 x 510510)

Let’s see if this takes us anywhere….πŸ™‚

Here are some sample primes written out in this form:

If anyone can spy any patterns I’m happy to hear them.πŸ™‚

Some more examples:

About petequinn

I'm a Canadian geotechnical engineer specializing in the study of landslides. I started this page to discuss some mathematical topics that interest me, initially this involved mostly prime numbers, but more recently I've diverted focus back to a number of topics of interest in geotechnique, geographic information systems and risk. I completed undergraduate training in engineering physics at Royal Military College (Kingston, Ontario), did a masters degree in civil (geotechnical) engineering at University of British Columbia (Vancouver), and doctorate in geological engineering at Queen's University (Kingston). I was a military engineer for several years at the beginning of my career, and did design and construction work across Canada and abroad. I've worked a few years for the federal government managing large environmental clean up projects in Canada's arctic, and I've worked across Canada, on both coasts and in the middle, as a consulting geotechnical engineer. My work has taken me everywhere in Canada's north, to most major Canadian cities and many small Canadian towns, and to Alaska, Chile, Bermuda, the Caribbean, Germany, Norway, Sweden, Bosnia, and Croatia. My main "hobby" is competitive distance running, which I may write about in future.
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One Response to A primorial-based place value number system

  1. Pingback: Elimination of primes within primorials through successive sieving | petequinnramblings

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