Mathematics desk
< November 26	<< Oct \| November \| Dec >>	Current desk >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

November 27

How much did UPS pay in workers comp claims for heat-related incidents last year? On the flip side, how much would it cost to air-condition their package vans and warehouses?

Did they also pay hazard bonuses for working in the heat?

Is it cheaper for UPS to just air condition their warehouses and package vans?

After paying the initial installation fees for the new HVAC systems, how much will it cost for UPS to run air conditioning and maintain their HVAC systems for one year (at least only when the weather is hot?)

And how much did they pay out in heat-related workers comp claims for one year?

How well will UPS come out ahead from simply air conditioning all places and vehicles that need air conditioned? --2600:8803:1D13:7100:BD6D:70D0:30AC:B227 (talk) 01:13, 27 November 2024 (UTC)[reply]

This is not a mathematics question. We don’t answer requests for opinions, predictions or debate. Dolphin (t) 04:59, 27 November 2024 (UTC)[reply]

The largest prime factor found by trial division

The largest prime factor found by Lenstra elliptic-curve factorization is 16559819925107279963180573885975861071762981898238616724384425798932514688349020287 of 7³³⁷+1 (see [1]), and the largest prime factor found by Pollard's p − 1 algorithm is 672038771836751227845696565342450315062141551559473564642434674541 of 960¹¹⁹-1 (see [2]), and the largest prime factor found by Williams's p + 1 algorithm is 725516237739635905037132916171116034279215026146021770250523 of the Lucas number L₂₃₆₆ (see [3]), but what is the largest prime factor found by trial division? (For general numbers, not for special numbers, e.g. 7*2^20267500+1 divides the number 12^{2^20267499}+1 found by trial division, but 12^{2^20267499}+1 is a special number since all of its prime factors are == 1 mod 2^20267500, thus the trial division only need to test the primes == 1 mod 2^20267500, but for general numbers such as 3*2¹⁰⁰+1, all primes may be factors) 61.229.100.16 (talk) 20:51, 27 November 2024 (UTC)[reply]

I don't have an answer, and Mersenne primes have properties that reduce the number of primes that need to be searched, meaning that it doesn't technically need full trial division, but I would nevertheless like to raise two famous examples which I'm fairly sure were done through manual checking:

In 1903, Frank Nelson Cole showed that $2^{67}-1$ is composite by going up to a blackboard and demonstrating by hand that it equals $193707721\times 761838257287$ . It took him "three years of Sundays" to do so, and I'm fairly sure he would have done it manually.
In 1951, Aimé Ferrier showed that ${\tfrac {2^{148}+1}{17}}$ is prime through use of a desk calculator, and I imagine a lot of handiwork.

GalacticShoe (talk) 02:29, 28 November 2024 (UTC)[reply]