Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Combining Primes
Replies: 81   Last Post: Aug 19, 2013 1:12 PM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Combining Primes
Posted: Aug 10, 2013 5:50 PM
 Plain Text Reply

On 10/08/2013 3:04 PM, Bart Goddard wrote:
> Sandy <sandy@hotmail.invalid> wrote in
> news:_I6dnb4o3esENZvPnZ2dnUVZ8sqdnZ2d@bt.com:
>

>> But suppose we leave the OPs second alternative to one side and ask
>> 'Is there any way to combine 2 primes to get a larger prime?' Given
>> the enormous number of ways two numbers can be "combined" to yield a
>> third, it would seem to be a hopeless task to give a negative answer.

>
> Indeed. E.g., let p and q be two distinct primes. Use the Euclidean
> algorithm to express their gcd as a linear combination of p and q,
> say, ap + bq =1. Multiply by 3 to get 3ap + 3bq =3, which is a prime.
> We have now combined two primes to obtain a third. So much for
> another crackpot's "resoundingly" false assertions.

Have you heard of AC (Axiom of Choice)?

What kind of "algorithm" that would allow you to _choose out of_
_UNCOUNTABLY many choices_ one particular choice for the 2-nary
relation (set) you'd symbolize by the less-than symbol '<'?

If you could do that, then you could "combine 2 primes to get a
larger prime" _in general_ .

But you can NOT.

--
-----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

Date Subject Author
8/10/13 jim
8/10/13 namducnguyen
8/10/13 namducnguyen
8/10/13 Sandy
8/10/13 namducnguyen
8/10/13 Sandy
8/10/13 namducnguyen
8/10/13 Sandy
8/10/13 Bart Goddard
8/10/13 Peter Percival
8/10/13 Bart Goddard
8/11/13 Peter Percival
8/11/13 namducnguyen
8/11/13 Bart Goddard
8/11/13 Peter Percival
8/11/13 fom
8/10/13 antani
8/10/13 Bart Goddard
8/10/13 namducnguyen
8/10/13 Bart Goddard
8/10/13 namducnguyen
8/10/13 Bart Goddard
8/10/13 namducnguyen
8/11/13 Peter Percival
8/11/13 namducnguyen
8/10/13 namducnguyen
8/11/13 Peter Percival
8/11/13 namducnguyen
8/11/13 Peter Percival
8/10/13 Virgil
8/10/13 Peter Percival
8/10/13 rossum
8/10/13 John
8/10/13 Helmut Richter
8/10/13 Helmut Richter
8/19/13 Phil Carmody
8/10/13 antani
8/11/13 Helmut Richter
8/10/13 Sandy
8/10/13 namducnguyen
8/11/13 Sandy
8/11/13 namducnguyen
8/11/13 Sandy
8/10/13 William Elliot
8/10/13 namducnguyen
8/10/13 William Elliot
8/11/13 namducnguyen
8/11/13 William Elliot
8/11/13 namducnguyen
8/11/13 William Elliot
8/11/13 namducnguyen
8/11/13 Sandy
8/11/13 namducnguyen
8/11/13 Sandy
8/11/13 namducnguyen
8/11/13 Sandy
8/11/13 namducnguyen
8/11/13 Sandy
8/11/13 namducnguyen
8/12/13 Sandy
8/12/13 Bart Goddard
8/13/13 Shmuel (Seymour J.) Metz
8/11/13 Sandy
8/19/13 Phil Carmody
8/11/13 Sandy
8/11/13 namducnguyen
8/11/13 Sandy
8/13/13 Shmuel (Seymour J.) Metz
8/11/13 Pubkeybreaker
8/11/13 Peter Percival
8/11/13 fom
8/11/13 Brian Q. Hutchings
8/12/13 namducnguyen
8/12/13 namducnguyen
8/12/13 Peter Percival
8/13/13 Shmuel (Seymour J.) Metz
8/12/13 Peter Percival
8/11/13 namducnguyen
8/11/13 namducnguyen
8/12/13 namducnguyen
8/12/13 Peter Percival
8/19/13 Phil Carmody

© The Math Forum at NCTM 1994-2018. All Rights Reserved.