7-million digit prime number discovered

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Discussion Overview

The discussion revolves around the recent discovery of a 7-million digit prime number, specifically a Mersenne prime, and touches on related concepts in number theory, such as the Prime Number Theorem and the search for larger primes. Participants explore the implications of this discovery and the methods used to find such primes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note the time and reward associated with the discovery of the 7-million digit prime, highlighting the ongoing search for even larger primes.
  • There is a suggestion that the focus on the Prime Number Theorem might be misplaced, with some arguing that a direct "prime solution" for generating all primes should be the objective.
  • Others challenge this view, questioning the relevance of the Prime Number Theorem to the topic of primality testing and the discovery of Mersenne primes.
  • One participant mentions the iterative method used to find new primes, indicating a lack of a simple equation for generating primes.
  • Another participant discusses the existence of convoluted formulae that can yield primes but are impractical for use.
  • There is confusion regarding the terminology used, particularly the term "prime solution," with some participants seeking clarification on its meaning.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and focus of the Prime Number Theorem in relation to the discovery of Mersenne primes. There is no consensus on whether a direct method for generating primes exists or if the current focus on iterative methods is appropriate.

Contextual Notes

Some participants express uncertainty about the definitions and implications of the Prime Number Theorem and related concepts, indicating a need for further clarification on these topics.

Who May Find This Useful

This discussion may be of interest to those studying number theory, particularly in the context of prime numbers and their properties, as well as individuals following advancements in computational mathematics.

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Viva ! Shoeless Jamie Joes !
 
i would have thought that was about goldbachs conjecture. but interesting none the less
 
FlatlineLemon said:
i would have thought that was about goldbachs conjecture. but interesting none the less

That's a millenium problem. It's worth much more than just a bunch of prize money.
 
My high school biology teacher always insisted that we say/write "cell duplication" and never "cell division".

Biology is the only science in which multiplication means the same thing as division.
 
Gokul43201 said:
My high school biology teacher always insisted that we say/write "cell duplication" and never "cell division".

Biology is the only science in which multiplication means the same thing as division.
trying to tease monique? :surprise: :biggrin:
 
Monique said:
http://www.newscientist.com/news/news.jsp?id=ns99995057

The time it took to calculate? 14 days, the reward? $100,000
now the wait is on for a 10-/100-million/1-billion digit prime number :eek:

I am in quantum physics (just trying to let you know my deficiencies), but I am following the Mersenne Prime search and have read a little about the Prime Number Theorem. Can you tell me the following?:

I've noticed the Prime Number Theorem effort seems entirely on the proof of how many primes below a certain number. But it seems to me the objective should be the prime solution (equation) for all primes and then the number of primes below a given number would be an outcome of a so-called "Prime Solution".

Do I have this backward? Is it too hard to get the Prime Solution directly so everyone is focused on the Prime Number Theorem. I am so glad you made this post. I was about to create my own from my current and complete confusion.
 
I've noticed the Prime Number Theorem effort seems entirely on the proof of how many primes below a certain number. But it seems to me the objective should be the prime solution (equation) for all primes and then the number of primes below a given number would be an outcome of a so-called "Prime Solution".

Come again? :confused: What "prime number theorem effort" (AFAIK, the prime number theorem has been proven. I'm not even sure how the prime number theorem relates to this topic, which seems to be mostly about primality testing and factoring integers)? What is "the" prime solution?
 
Clearly then, I am indeed off-track. However, I was responding to the initial entry of this thread from Monique - the latest Mersene prime. My understanding is that each new prime is found by iteration...every computer involved takes the next possible Mersenne prime and tests its primality. So I assumed that there must not be an equation for generating the primes in a simple way aside from an iterative method. But I can not find any reference to this. Therefore I was wondering, is there a prime solution or theoretical effort in this area? I am quite possibly still on the wrong track...can you help me?
 
  • #10
i think to my knowledge that the largest twin primes known to date are 33218925*2^169690 +-1. (that is 51090 digits)!

muzza i think you are referring to the prime number theorem? or are you making a reference to the infinitude of primes theorem? they are much different, and give you information on primes, but is that needed to talk about this mersenne prime discovery?
 
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  • #11
There are formulae involving many variables whose positive values are exactly the primes. They are too convoluted and take too long to use to be of any use (given a set of input values, you have no a priori reason for expecting the output to be positive). Not all primes are Mersenne anyway (obviously almost none are going to be mersenne, in some sense). You are still misusing the word solution, and no there is obviously no (known) pattern in the Mersenne numbers that tells you which will be the prime ones.
 
  • #12
muzza i think you are referring to the prime number theorem?

Uh, yes, when I say "prime number theorem", I do mean the "prime number theorem".

or are you making a reference to the infinitude of primes theorem? they are much different, and give you information on primes, but is that needed to talk about this mersenne prime discovery?

I'll be damned if I know, I was asking the exact same question ;)
 
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