Prime number needs

General discussion about calculators, SwissMicros or otherwise
User avatar
Walter
Posts: 1735
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

Prime number needs

Post by Walter »

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 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
rprosperi
Posts: 1070
Joined: Mon Apr 24, 2017 7:48 pm
Location: New York

Re: Prime number needs

Post by rprosperi »

Walter wrote:
Mon Mar 16, 2020 11:43 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 & 00656, DM10L: 071/100
User avatar
Walter
Posts: 1735
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

Re: Prime number needs

Post by Walter »

rprosperi wrote:
Tue Mar 17, 2020 3:30 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 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
User avatar
H2X
Posts: 609
Joined: Tue Apr 25, 2017 8:00 am
Location: Norway

Re: Prime number needs

Post by H2X »

rprosperi wrote:
Tue Mar 17, 2020 3:30 am
Walter wrote:
Mon Mar 16, 2020 11:43 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 C43 | DM41X #50 | various HP models
The earth is flat. It just appears round because it is massive and curves spacetime.
User avatar
Walter
Posts: 1735
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

Re: Prime number needs

Post by Walter »

H2X wrote:
Tue Mar 17, 2020 5:26 pm
rprosperi wrote:
Tue Mar 17, 2020 3:30 am
Walter wrote:
Mon Mar 16, 2020 11:43 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 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
User avatar
pauli
Posts: 122
Joined: Tue May 02, 2017 10:11 am
Location: Australia

Re: Prime number needs

Post by pauli »

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
User avatar
Walter
Posts: 1735
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

Re: Prime number needs

Post by Walter »

pauli wrote:
Wed Mar 18, 2020 11:00 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 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
rprosperi
Posts: 1070
Joined: Mon Apr 24, 2017 7:48 pm
Location: New York

Re: Prime number needs

Post by rprosperi »

pauli wrote:
Wed Mar 18, 2020 11:00 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 & 00656, DM10L: 071/100
User avatar
Walter
Posts: 1735
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

Re: Prime number needs

Post by Walter »

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 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
User avatar
Mark Hardman
Posts: 116
Joined: Wed May 03, 2017 3:26 am
Location: Houston, TX

Re: Prime number needs

Post by Mark Hardman »

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, 00445
DM10L: 017/100, DM11L: 00121, DM12L: 02005, DM15L: 00523, DM16L: 00008, DM41L: 00111
Post Reply