## Old HPMuseum HP-30b primality test on the 41x

Discussion about the new DM41X calculator
Over_score
Posts: 108
Joined: Fri May 05, 2017 9:37 pm
Location: France

### Re: Old HPMuseum HP-30b primality test on the 41x

Mark Hardman wrote:
Tue May 05, 2020 10:30 pm
Does "probable" only include false positives or is there a possibility of false negatives as well?
False definitely means composite.
True definitely means prime if n ≤ 3 317 044 064 679 887 385 961 981 and probably prime else.
The probability of a false positive is less than 1/(4^k), k is the number of tests being done. In our case we do 25 tests, so 1/(4^25) ≃ 8.9×10^(-16)
Last edited by Over_score on Wed May 06, 2020 11:19 am, edited 1 time in total.
DM42 (SN 00284 & 03835), DM15L, HP41CV, HP42S, HP35s, WP34S, HP Prime
pauli
Posts: 119
Joined: Tue May 02, 2017 10:11 am
Location: Australia

### Re: Old HPMuseum HP-30b primality test on the 41x

No prime number will ever be claimed to be composite. Some composite numbers will be claimed to be prime.

As @Over_score notes the probability of falsely claiming a composite to be prime is 4^-25. Since the test is deterministic, it will always report the same false positives.

Pauli
jonmoore
Posts: 106
Joined: Mon Apr 13, 2020 4:18 pm

### Re: Old HPMuseum HP-30b primality test on the 41x

jonmoore wrote:
Tue May 05, 2020 10:50 pm

At 31 digits it would appear to be into the realm of the probable. But to be frank I'd be even more spooked if the 43s answers in the affirmative as to the identity of Belphegor's prime.
Walter
Posts: 1715
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

### Re: Old HPMuseum HP-30b primality test on the 41x

jonmoore wrote:
Wed May 06, 2020 4:11 pm
jonmoore wrote:
Tue May 05, 2020 10:50 pm

At 31 digits it would appear to be into the realm of the probable. But to be frank I'd be even more spooked if the 43s answers in the affirmative as to the identity of Belphegor's prime.
Didn't we read that yesterday already? But how shall you know what you wrote before you can read it once more?
DM42 SN: 00041 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
jonmoore
Posts: 106
Joined: Mon Apr 13, 2020 4:18 pm

### Re: Old HPMuseum HP-30b primality test on the 41x

User error on my part Walter. I was editing the message to add the smiley at the the end of the message as I worried that people might have taken my original response seriously (I obviously pressed the Quote function rather than the Edit). That'll learn me to not attempt to disguise my lame attempts at humour.