Prime number needs

General discussion about calculators, Swiss Micros or otherwise
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Walter
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Prime number needs

Post by Walter » Mon Mar 16, 2020 10:43 pm

There is a binary test called PRIME? on the WP34S (yes, the old one). It works fine there since "the method is believed to work for integers up to 9E18" as stated in its manual. I checked with DBLON and found primes at 9'000'000'000'000'000'053, ...157, ...191, ...317, etc. up to 9'223'372'036'854'775'783. The latter is the maximum prime found by the WP34S.

For the WP43S we've implemented a procedure working up to 3'317'044'064'679'887'385'961'981. This means almost 6 orders of magnitude more than the WP34S covers. Does anybody need even greater primes? If yes, how great and what for?
DM42 SN: 00041 --- Follower of Platon.

HP-35, HP-45, ..., HP-50, WP 34S, WP 31S, DM16L

rprosperi
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Re: Prime number needs

Post by rprosperi » Tue Mar 17, 2020 2:30 am

Walter wrote:
Mon Mar 16, 2020 10:43 pm
For the WP43S we've implemented a procedure working up to 3'317'044'064'679'887'385'961'981. This means almost 6 orders of magnitude more than the WP34S covers. Does anybody need even greater primes? If yes, how great and what for?
LOL. No one needs any primes at all. I think the question you intend to ask is: "Does anybody whimsically desire even greater primes?" To which the answer will almost certainly be yes. I look forward to reading the uses and justification.

Keep it up team 43S!
--bob p

DM42: β00071 & 00282, DM41X: β00071, DM10L: 071/100

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Walter
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Re: Prime number needs

Post by Walter » Tue Mar 17, 2020 10:03 am

rprosperi wrote:
Tue Mar 17, 2020 2:30 am
No one needs any primes at all. I think the question you intend to ask is: "Does anybody whimsically desire even greater primes?" To which the answer will almost certainly be yes. I look forward to reading the uses and justification.
They hide in the bushes and don't dare showing up :lol:
DM42 SN: 00041 --- Follower of Platon.

HP-35, HP-45, ..., HP-50, WP 34S, WP 31S, DM16L

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H2X
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Re: Prime number needs

Post by H2X » Tue Mar 17, 2020 4:26 pm

rprosperi wrote:
Tue Mar 17, 2020 2:30 am
Walter wrote:
Mon Mar 16, 2020 10:43 pm
For the WP43S we've implemented a procedure working up to 3'317'044'064'679'887'385'961'981. This means almost 6 orders of magnitude more than the WP34S covers. Does anybody need even greater primes? If yes, how great and what for?
LOL. No one needs any primes at all. I think the question you intend to ask is: "Does anybody whimsically desire even greater primes?" To which the answer will almost certainly be yes. I look forward to reading the uses and justification.
I want to set a new Guinness World Record. You asked... 8-)
DM42 #40 running WP43C | DM41X #50
The earth is flat. It just appears round because it is massive and curves spacetime.

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Walter
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Re: Prime number needs

Post by Walter » Tue Mar 17, 2020 5:37 pm

H2X wrote:
Tue Mar 17, 2020 4:26 pm
rprosperi wrote:
Tue Mar 17, 2020 2:30 am
Walter wrote:
Mon Mar 16, 2020 10:43 pm
For the WP43S we've implemented a procedure working up to 3'317'044'064'679'887'385'961'981. This means almost 6 orders of magnitude more than the WP34S covers. Does anybody need even greater primes? If yes, how great and what for?
LOL. No one needs any primes at all. I think the question you intend to ask is: "Does anybody whimsically desire even greater primes?" To which the answer will almost certainly be yes. I look forward to reading the uses and justification.
I want to set a new Guinness World Record. You asked... 8-)
Declined for lack of use and justification 8-)
DM42 SN: 00041 --- Follower of Platon.

HP-35, HP-45, ..., HP-50, WP 34S, WP 31S, DM16L

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pauli
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Re: Prime number needs

Post by pauli » Wed Mar 18, 2020 10:00 am

I use far larger primes in my day job.

The 34S limits it prime testing to 2⁶³ from memory due to a problem in my implementation of the test.

Pauli

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Walter
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Re: Prime number needs

Post by Walter » Wed Mar 18, 2020 10:29 am

pauli wrote:
Wed Mar 18, 2020 10:00 am
I use far larger primes in my day job.

The 34S limits it prime testing to 2⁶³ from memory due to a problem in my implementation of the test.
1. How far is far?? (Good grief, we're talking about numbers here, aren't we? :roll: )
2. The actual limit of the 34S is found above - no need for stressing memory.
DM42 SN: 00041 --- Follower of Platon.

HP-35, HP-45, ..., HP-50, WP 34S, WP 31S, DM16L

rprosperi
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Re: Prime number needs

Post by rprosperi » Wed Mar 18, 2020 12:55 pm

pauli wrote:
Wed Mar 18, 2020 10:00 am
I use far larger primes in my day job.
Interesting! To the extent that you can, plz tell us what they are used for. Presumably some form of encryption, but it would be really interesting to find out if they are useful in other applications.
--bob p

DM42: β00071 & 00282, DM41X: β00071, DM10L: 071/100

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Walter
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Re: Prime number needs

Post by Walter » Fri Mar 20, 2020 9:38 pm

Beyond cryptographic applications, we're looking forward to whoever can name another use of great primes ("great" as specified above). 8-) 8-)
DM42 SN: 00041 --- Follower of Platon.

HP-35, HP-45, ..., HP-50, WP 34S, WP 31S, DM16L

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Mark Hardman
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Re: Prime number needs

Post by Mark Hardman » Sat Mar 21, 2020 12:16 am

From the Wikipedia article on the Mersenne Twister pseudo-random number generator:

The most commonly used version of the Mersenne Twister algorithm is based on the Mersenne prime 2^(19937)−1.

It also appears that large primes are used for the Lehmer random number generator:

Mersenne primes 2^31−1 and 2^61−1 are popular, as are 2^32−5 and 2^64−59

Though these four primes fall far short of the "great" categorization.
DM42: β00043, β00065, 00357
DM41X: β00054

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