A Question About Primes

[RocketManJames]

So, today I was chatting with another 2p2er... and somehow I went off-track and thought about this 'special' type of prime number. Bear with me, this might be a totally stupid thing, but here it is.

Take the following 2 numbers:

111103 and 419743

Both are prime (I looked them up).

But, they are also prime in various concatenations...

111103: (11 | 1103) or (11 | 11 | 03) -- prime on 3 levels

419743: (41 | 9743) or (419 | 743) or (41 | 97 | 43) -- prime on 4 levels

Now, my question... is there a term for this? Or is it just some useless observation I made? I mean, it'd be pretty neat if these types of primes were 'magical' (for lack of a better term) in some way.

-RMJ

[pokergrader]

You have invented it and you get to make a term for it. Make a wikipedia entry for your discovery and it is all yours.

[Duke]

The only reason a Mersenne Prime would be more "useful" than this is the correlation with perfect numbers. Find a correlation with something else and name this after yourself.

~D

[bunny]

Neat

[madnak]

It seems like the property depends on the number system. For example, different primes would probably qualify under octal rather than decimal.

[RocketManJames]

[ QUOTE ]
The only reason a Mersenne Prime would be more "useful" than this is the correlation with perfect numbers. Find a correlation with something else and name this after yourself.

~D

[/ QUOTE ]

Well, as we were talking about earlier... it's like numbers with the 'Mersenne form' had a good chance to be prime, so maybe certain concatenations of primes are also likely candidates to be prime.

I really have no idea. I am just throwing out a few thoughts.

Edit: I was just told that there aren't that many Mersenne primes, and so when I said "good chance" earlier, I was totally wrong.

-RMJ

[chezlaw]

[ QUOTE ]
Edit: I was just told that there aren't that many Mersenne primes, and so when I said "good chance" earlier, I was totally wrong.

[/ QUOTE ]
There's possibly an infinite number of mersenee primes. Unproved afaik.

chez

[Duke]

[ QUOTE ]
[ QUOTE ]
Edit: I was just told that there aren't that many Mersenne primes, and so when I said "good chance" earlier, I was totally wrong.

[/ QUOTE ]
There's possibly an infinite number of mersenee primes. Unproved afaik.

chez

[/ QUOTE ]

Well, yeah, but we were talking about Mersenne primes : all numbers of the form 2^p-1, where p is prime. That's a pretty small fraction. Not common in that sense.

~D

[Copernicus]

To be worthy of a name it should be prime in all possible parsings, not just some.

[Duke]

[ QUOTE ]
To be worthy of a name it should be prime in all possible parsings, not just some.

[/ QUOTE ]

And yet there still might be more than 43 of them if we limit ourselves to 10 million digit numbers.

~D

[pzhon]

Problems like this that depend on the base are usually not taken seriously within mathematics. There are numerous articles on primes with repeated digits in the Journal of Recreational Mathematics, and I would not be surprised if there were some discussion there of primes built by concatenating primes.

[srjunkacct]

"Base 8 is just like base 10, really...if you're missing two fingers."

-- Tom Lehrer, "New Math"

[Siegmund]

I would hesitate to say that "problems that depend on the base" are not taken seriously in mathematics. The Mersennes are where two families of special numbers coincide, the k^n-1 family which is investigated for other prime values of k, and the 'repunits', (k^n-1)/(k-1), which can be interesting for both prime and composite k. They all share some common features -- n must be prime in order for k^n-1 to be for instance.

Things which depend on "typographical" rather than "mathematical" properties do tend to be more recreationally oriented.

The OP might want to google Al Zimmermann's Programming Contests, and read about their contest last winter to find a grid of digits which contained the largest number of distinct primes ... they were very interested in prime numbers which contained other primes inside them in this way.

[CrayZee]

Coin the term "Bounded Concatenated Primes", "Arbitrarily Concatenated Primes", or "Complete Arbitrarily Concatenated Primes", and you'll sound smurt! /images/graemlins/smile.gif

Create you own useless set of primes and you'll be famous!!