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Old 2018-12-07, 02:02   #1
3.14159
 
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Default records for primes

is there a list of records for the largest "random" primes ever discovered?

primes like this, for example:
Code:
603174145752094582013717026896404708075695200061888275740347912686132908983076912951364116014048644080780955692362443280745657218075567353486762269085008456050044645237568700267765675637155099757211742917240791004903205625152309314304699426586676846234879151913802061712891194848272697216649646754717

Last fiddled with by 3.14159 on 2018-12-07 at 02:06 Reason: clarify!
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Old 2018-12-07, 03:15   #2
rudy235
 
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Quote:
Originally Posted by 3.14159 View Post
is there a list of records for the largest "random" primes ever discovered?

primes like this, for example:
Code:
603174145752094582013717026896404708075695200061888275740347912686132908983076912951364116014048644080780955692362443280745657218075567353486762269085008456050044645237568700267765675637155099757211742917240791004903205625152309314304699426586676846234879151913802061712891194848272697216649646754717
There are no Random primes. Unless that by random you mean "not of a special form".

If that is what you mean there are primes of the form xy+yx where x is odd and y is even (or vice-versa) and have no common factor.
Or a*bc± N where a and b are small numbers, c is an ordinary number and N is another ordinary number. (greater than1)

An example of the first kind is 67535122+ 51226753 of 25,050 digits
Of the second kind is 2116224+15905 of almost 35,000 digits.

Both of these kinds of numbers are not easy to prove prime and need to use a "general method like ECPP to prove them prime. However, they are still easy to express with an arithmetical formula.

However a number like this one that has over 34,000 digits cannot be expressed with a mathematical formula (a simple one that is) and also needs ECPP to prove it as prime.

So I suggest you look at the list of primes proven by ECPP in the Chris Caldwell webpage and see what you can find. You can start here or here
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Old 2018-12-07, 05:21   #3
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Another method available for numbers not of a special form is Mihăilescu's CIDE. Sadly, no public implementations are available, and as far as I can tell no work is being done on this interesting (and promising?) method.
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Old 2018-12-07, 05:25   #4
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Quote:
Originally Posted by rudy235 View Post
So I suggest you look at the list of primes proven by ECPP in the Chris Caldwell webpage
Elliptic Curve Primality Proof

See also Henri & Renaud Lifchitz's PRP Top records for probable-primes, which are typically of no special form (but lack a primality proof).
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Old 2018-12-07, 22:24   #5
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Quote:
Originally Posted by rudy235 View Post
However a number like this one that has over 34,000 digits cannot be expressed with a mathematical formula (a simple one that is) and also needs ECPP to prove it as prime.
Dr Sardonicus writes to me saying he can't access the prime. I can't explain why because it does work for me. Try this and once there click on the third item on the list... Picture(57885161)
34093 decimal digits
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Old 2018-12-07, 23:59   #6
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Quote:
Originally Posted by rudy235 View Post
Dr Sardonicus writes to me saying he can't access the prime. I can't explain why because it does work for me. Try this and once there click on the third item on the list... Picture(57885161)
34093 decimal digits
Hmm. That works fine and dandy. The original link to the picture a few posts back also works -- now!
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Old 2018-12-08, 17:49   #7
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The server is doing something funny. If I click on http://www.ellipsa.eu/public/primo/f...-57885161.html (the original link) I get
Code:
Forbidden

You don't have permission to access /public/primo/files/picture-57885161.html on this server.
Apache/2.4.10 (Ubuntu) Server at www.ellipsa.eu Port 80
If I click on http://www.ellipsa.eu/public/primo/top20.html then on the Picture(57885161) link it works. If I then click on the original link it will work, until I close the Picture(57885161) page. Then clicking on the original link fails again.

Checking on another computer while I have the link from Picture(57885161) open on this computer I get the same pattern. So it must be putting something, probably a cookie, onto the system when you click on the Picture(57885161) link (both computers connect through the same router so the server will see them coming from the same IP address.

But the original link sometimes still works for a few seconds after closing the Picture(57885161) link. Curiouser and curiouser.

Chris
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Old 2018-12-08, 23:39   #8
3.14159
 
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Quote:
If that is what you mean there are primes of the form xy+yx where x is odd and y is even (or vice-versa) and have no common factor.
Or a*bc± N where a and b are small numbers, c is an ordinary number and N is another ordinary number. (greater than1)
well, i should have been more clear about what I was talking about. I meant "random" as in, something like this:

Code:
In[6]:= RandomPrime[{10^49, 10^50}]
Out[6]= 27101114565622859841940858633057180407935116844491
i was wondering bc i found a "random" prp15000

Last fiddled with by 3.14159 on 2018-12-08 at 23:43 Reason: clarify #2
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Old 2018-12-09, 00:08   #9
Batalov
 
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This one is totally random ... and prime.
Attached Files
File Type: txt random42k.txt (41.9 KB, 41 views)
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