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Mathematicians outwit hidden number conspiracy

#1
C C Offline
https://www.quantamagazine.org/mathemati...-20220103/

INTRO: A new proof has debunked a conspiracy that mathematicians feared might haunt the number line. In doing so, it has given them another set of tools for understanding arithmetic’s fundamental building blocks, the prime numbers.

In a paper posted last March, Harald Helfgott of the University of Göttingen in Germany and Maksym Radziwiłł of the California Institute of Technology presented an improved solution to a particular formulation of the Chowla conjecture, a question about the relationships between integers.

The conjecture predicts that whether one integer has an even or odd number of prime factors does not influence whether the next or previous integer also has an even or odd number of prime factors. That is, nearby numbers do not collude about some of their most basic arithmetic properties.

That seemingly straightforward inquiry is intertwined with some of math’s deepest unsolved questions about the primes themselves. Proving the Chowla conjecture is a “sort of warmup or steppingstone” to answering those more intractable problems, said Terence Tao of the University of California, Los Angeles.

And yet for decades, that warmup was a nearly impossible task itself. It was only a few years ago that mathematicians made any progress, when Tao proved an easier version of the problem called the logarithmic Chowla conjecture. But while the technique he used was heralded as innovative and exciting, it yielded a result that was not precise enough to help make additional headway on related problems, including ones about the primes. Mathematicians hoped for a stronger and more widely applicable proof instead.

Now, Helfgott and Radziwiłł have provided just that. Their solution, which pushes techniques from graph theory squarely into the heart of number theory, has reignited hope that the Chowla conjecture will deliver on its promise — ultimately leading mathematicians to the ideas they’ll need to confront some of their most elusive questions... (MORE - details)
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#2
shadow Offline
dear family,

the decimal number system has ten symbols (dec- means ten).

0 is symbol 1, 1 is symbol 2, 2 is symbol 3...

0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10

0 to 9 are used then you use symbol 1 and symbol 0 again to make 10. then you use symbol 1 and symbol 1 again to make 11, then you use symbol 1 and symbol 2 again to make 12 and so on.

computers use BInary digiTs called bits. bi-nary has 2 numbers (bi- means 2 and -nary means numbers). bi-nary has 0 and 1. 0 is position 1 and 1 is position 2.

0-1
1-2

bits are switches that are either 0 (off) or 1 (on).

numbers are written from right-to-left on the top and doubled (added to itself) each time...

128|64|32|16|8|4|2|1

so 1+1 is 2, 2+2 is 4, 4+4 is 8...

when there is a binary 0 there is that number not and when there is a 1 there is that number.

00001010

is one 8, zero 4, one 2 and zero 1

8+2

10

computer programs are written in hexadecimal. hex means six and decimal means ten. six and ten is sixteen. there are sixteen hexadecimal number. 0 to 9 then A, B, C, D, E and F

0 is number 1 and F is number 16

0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10
A-11
B-12
C-13
D-14
E-15
F-16

0 to F are zero to fifteen then a 1 is put to the left and a 0 on the right for sixteen, a 1 and a 1 for seventeen, a 1 and a 2 for eighteen and so on.

a computer program checks the hexadecimal numbers to ASCII (American Standard Code for Information Interchange) that is on a chip and the hexidecimal numbers are a computer order, a letter, a number or a symbol (# for example). computer programs can be written in this way.

love from Peter
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#3
stryder Offline
Peter,
you do have a habit of creating posts which literally have no meaning to the casual observer (Thus why previously I have closed/crippled accounts). It's like you try to say something on an inner thought you have but kind of miss out an entire chunk of what the message is about or more concerningly are just trolling with nonsense. (I prefer the attempts at being actually communicative over just being a bot rip off.)

If you are going to talk about the difference between binary-decimal-hexidecimal at least refer to it as base. (base-2 | base-10 | base-16)

The Base (or Radix) is important as it goes beyond just a cannonical value and actually represents it's mathematical position. That's why in cryptology (including compression algorithms) base is often refered to (e.g. Base64 or 256-bit Encryption etc)

Anyway please, please please try to post as if you are dealing with another human being, not something that can fill in the gaps based upon your own mnemonics.

Regards,
Stryder
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