Prime Numbers Not So Random?

Jeff Moriarty writes "Some physicists believe they might have caught a whiff of a pattern in the sequence of prime numbers. This would have a huge impact across mathematics, and to people who just really like primes... or like being Prime."

Comments

anyone else getting the feeling...

[ddd2k]

the interval thing seemed like such a trivial observation. surely many others have easily noticed that. Its another "I think i discovered a pattern" claim, while still have no way to prove it.

Re:anyone else getting the feeling...

[Smidge204]

Proof: All odd numbers are prime.

Mathematitian: "1 is prime, 3 is prime, 5 is prime, 7 is prime. The rest are prime by induction."

Physisist: "1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is not but is likely to be experimental error, 11 is prime, 13 is prime..."

Engineer: ""1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime to a reasonable degree of accuracy, 11 is prime, 13 is prime..."

Computer Scientist: "1 is prime, 1 is prime, 1 is prime, 1 is prime..."

</joke>
=Smidge=

Here's the rub

[Anonymous Coward]

Here's the problem with finding patterns in Primes: It has to do with the way most things in number theory are formulated. Prime numbers are figured out by a process of non-definition and NOT by some form of additive process. An example or two might make that statement a bit clearer:

If I needed, for example, to find a rule that returns only even numbers, my problem is simplicity itself, I have no need to test a given number to determine whether or not it is even, I can force it to be even by applying any number of simple (or complex) formulas that work within the system.

If someone gives me number X, I have no need to know what X is, all I have to do is multiply X by 2 and (after a little inductive reasoning), I have guaranteed that I now have an even number.

Prime numbers are NOT found that way. An even number is determined to have the property 'evenness' from within the number system itself, namely multiplication by 2. It is a simple additive process to include other even numbers into a given set. A prime number on the other hand, forgive the inexactness, can be considered to have the inherent property 'whatever property that created me that is unique to me'.

IOW, each prime number is unalterably unique and furthermore it is unique in a way which is unique to EACH AND EVERY prime number, all by itself. No other prime number has the same property that makes any other prime number unique.

EXAMPLES (bad, I know, but the best I could do at 0430):
the number 7 (a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 7 and 1, a property that it shares with no other numbers.

the number 17 (a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 17 and 1, a property that it shares with no other numbers.

the number 21 (not a prime) has the property (among other properties, like 'oddness') that it has the divisors (7 and 3) AND (21 and 1). Only primes get to leave out that AND part.

The prime numbers are the GAPS within the number-system (and in a rather pathological side note - they are also the glue that holds the system together). The definition of a prime number is, put simplistically: ANY number X that is NOT composite.

Saying you have found a pattern in the prime numbers is tantamount to saying that you have a rule that can create prime numbers W/O checking to see if it's true or not. Put another way, it is exactly the same as saying:

"I have a formula P(x) that can always churn out primes, give me a number, any number and after the application of my formula, I can guarantee that it will be a prime number."

If you could do that, I have a whole bunch of NP complete problems for you to work on (and a bone to pick with a certain Mr. Godel).

Any pattern w/in the set of prime numbers would be a formula with an infinite number of rules (an individual rule for each individual prime number, AT LEAST), and anything with an infinite number of rules can be considered completely, totally and irrevocably RANDOM.

Some late night ramblings from a guy who's too tired and lazy to log on.

Re:I found a pattern!

[itsme1234]

Of course they are prime ! ANY number is either:

6n (not prime of course)
6n+1
6n+2 (not prime of course)
6n+3 (not prime of course)
6n+4 (not prime of course)
6n+5

And 6n+5 is the same as 6(n+1)-1 so indeed you are right. You deserve a price for finding a 6th grade theorem.

How to prove that all odd numbers are prime

[dargaud]

"It was mentioned on CNN that the new prime number discovered recently is four times bigger than the previous record." John Blasik

"You know what seems odd to me? Numbers that aren't divisible by two." Michael Wolf.

"I don't get even, I get odder."

Well, the problem "How to prove that all odd numbers are prime" has different solutions whether you are a:

Mathematician: 1 is prime, 3 is prime, 5 is prime, 7 is prime, and by induction we have that all the odd integers are prime.

Physicist: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is an experimental error...

Engineer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime...

Chemist: 1 prime, 3 prime, 5 prime... hey, let's publish!

Modern physicist using renormalization: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... 9/3 is prime, 11 is prime, 13 is prime, 15 is ... 15/3 is prime, 17 is prime, 19 is prime, 21 is ... 21/3 is prime...

Quantum Physicist: All numbers are equally prime and non-prime until observed.

Professor: 1 is prime, 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.

Confused Undergraduate: Let p be any prime number larger than 2. Then p is not divisible by 2, so p is odd. QED

Measure nontheorist: There are exactly as many odd numbers as primes (Euclid, Cantor), and exactly one even prime (namely 2), so there must be exactly one odd nonprime (namely 1).

Cosmologist: 1 is prime, yes it is true....

Computer Scientist: 1 is prime, 10 is prime, 11 is prime, 101 is prime...

Programmer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 will be fixed in the next release, ...

C programmer: 01 is prime, 03 is prime, 05 is prime, 07 is prime, 09 is really 011 which everyone knows is prime, ...

BASIC programmer: What's a prime?

COBOL programmer: What's an odd number?

Windows programmer: 1 is prime. Wait...

Mac programmer: Now why would anyone want to know about that? That's not user friendly. You don't worry about it, we'll take care of it for you.

Bill Gates: 1. No one will ever need any more than 1.

ZX-81 Computer Programmer: 1 is prime, 3 is prime, Out of Memory.

Pentium owner: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 8.9999978 is prime...

GNU programmer: % prime
usage: prime [-nV] [--quiet] [--silent] [--version] [-e script] --catenate --concatenate | c --create | d --diff --compare | r --append | t --list | u --update | x -extract --get [ --atime-preserve ] [ -b, --block-size N ] [ -B, --read-full-blocks ] [ -C, --directory DIR ] [--checkpoint ] [ -f, --file [HOSTNAME:]F ] [ --force-local ] [ -F, --info-script F --new-volume-script F ] [-G, --incremental ] [ -g, --listed-incremental F ] [ -h, --dereference ] [ -i, --ignore-zeros ] [ --ignore-failed-read ] [ -k, --keep-old-files ] [ -K, --starting-file F ] [ -l, --one-file-system ] [ -L, --tape-length N ] [ -m, --modification-time ] [ -M, --multi-volume ] [ -N, --after-date DATE, --newer DATE ] [ -o, --old-archive, --portability ] [ -O, --to-stdout ] [ -p, --same-permissions, --preserve-permissions ] [ -P, --absolute-paths ] [ --preserve ] [ -R, --record-number ] [ [-f script-file] [--expression=script] [--file=script-file] [file...]
prime: you must specify exactly one of the r, c, t, x, or d options
For more information, type "prime --help''

Unix programmer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, ...
Segmentation fault, Core dumped.

Computer programmer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is ...