December2025 - Challenge
This puzzle was suggested by Giorgos Kalogeropoulos - thanks!
Given a natural number n, take the first n odd primes (3,5,7,11\ldots ) and the first n positive even integers (2,4,\ldots,2n).
Compute all possible pairwise sums between these two sets (n^2 sums in total, all odd).
We denote by f(n) the number of these sums that are prime. For example, f(5)=16.
Your goal: Find f(10^8).
A bonus "*" will be given for finding f(10^9).
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!
We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com
Challenge:
01/12/2025 @ 13:10 PM EST
Solution:
05/01/2025 @ 12:00 AM EST
List Updated:
05/01/2026 @ 12:10 PM EST
*Lazar Ilic(1/12/2025 2:51 PM IDT)
*Jiri Spitalsky(1/12/2025 4:34 PM IDT)
*Daniel Chong Jyh Tar(1/12/2025 4:39 PM IDT)
*Dan Dima(1/12/2025 4:45 PM IDT)
Ahmet Yuksel(1/12/2025 6:37 PM IDT)
*Bertram Felgenhauer(1/12/2025 8:07 PM IDT)
*Hongcheng Zhu(1/12/2025 9:35 PM IDT)
*Nadir S.(1/12/2025 10:35 PM IDT)
*Prashant Wankhede(1/12/2025 11:40 PM IDT)
*King Pig(2/12/2025 12:30 AM IDT)
*Stephen Ebert(2/12/2025 12:37 AM IDT)
*Sanandan Swaminathan(2/12/2025 1:20 AM IDT)
*Naftali Peles(2/12/2025 2:09 AM IDT)
*Alper Halbutogullari(2/12/2025 2:42 AM IDT)
*Guangxi Liu(2/12/2025 4:42 AM IDT)
*Bert Dobbelaere(2/12/2025 9:38 AM IDT)
Reiner Martin(2/12/2025 12:20 PM IDT)
Stéphane Higueret(2/12/2025 1:03 PM IDT)
*Vladimir Volevich(2/12/2025 1:42 PM IDT)
*Daniel Bitin(2/12/2025 2:37 PM IDT)
*Karl-Heinz Hofmann(2/12/2025 5:19 PM IDT)
*Shirish Chinchalkar(2/12/2025 5:51 PM IDT)
*Latchezar Christov(2/12/2025 6:02 PM IDT)
*Ankit Aggarwal(2/12/2025 8:07 PM IDT)
*Paul Lupascu(2/12/2025 8:24 PM IDT)
*Arthur Vause(2/12/2025 8:49 PM IDT)
*James Pepper(2/12/2025 10:14 PM IDT)
Lorenz Reichel(2/12/2025 10:41 PM IDT)
*Martin Thorne(3/12/2025 12:24 AM IDT)
*David F.H. Dunkley(3/12/2025 1:56 AM IDT)
Gary M. Gerken(3/12/2025 10:37 AM IDT)
*Sergey Batalov(3/12/2025 11:29 AM IDT)
*Loukas Sidiropoulos(3/12/2025 4:08 PM IDT)
*Juergen Koehl(3/12/2025 6:08 PM IDT)
*Lorenzo Gianferrari Pini(3/12/2025 6:10 PM IDT)
Paul Shaw(3/12/2025 7:02 PM IDT)
*Kang Jin Cho(4/12/2025 7:34 AM IDT)
*Dieter Beckerle(4/12/2025 8:24 AM IDT)
Fabio Michele Negroni(4/12/2025 12:18 PM IDT)
*Dominik Reichl(4/12/2025 6:33 PM IDT)
*Hugo Pfoertner(4/12/2025 7:33 PM IDT)
Amos Guler(4/12/2025 8:46 PM IDT)
*Özgür Soysal(5/12/2025 9:04 AM IDT)
*Michael Vahle(5/12/2025 4:40 PM IDT)
*Mitja Devetak(5/12/2025 6:14 PM IDT)
*John Spurgeon(6/12/2025 7:16 AM IDT)
*Titos Betsos(6/12/2025 5:16 PM IDT)
*Eran Vered(6/12/2025 10:53 PM IDT)
*Liubing Yu(7/12/2025 3:52 AM IDT)
*Peter Jin(7/12/2025 7:17 AM IDT)
*Prakhar Kapoor(7/12/2025 12:24 PM IDT)
*Michael Liepelt(7/12/2025 7:46 PM IDT)
Alex Fleischer(7/12/2025 9:17 PM IDT)
*Chris Shannon(7/12/2025 11:42 PM IDT)
*Michael Ott(8/12/2025 3:40 AM IDT)
*Shouky Dan & Tamir Ganor(8/12/2025 10:21 AM IDT)
*Wyatt Daviau(8/12/2025 6:27 PM IDT)
*José Eduardo Gaboardi de Carvalho(8/12/2025 9:29 PM IDT)
*Gürkan Koray Akpınar(10/12/2025 9:19 PM IDT)
Yanrui (Kevin) Li(11/12/2025 4:03 AM IDT)
*Guillaume Dujardin(11/12/2025 12:36 PM IDT)
Piyush Agrawal(11/12/2025 2:37 PM IDT)
*Laurent Desnogues(11/12/2025 7:09 PM IDT)
*Nyles Heise(12/12/2025 6:08 AM IDT)
*Hansraj Nahata & Govind Jujare(13/12/2025 4:12 AM IDT)
*Joaquim Carrapa(13/12/2025 5:38 PM IDT)
*Viplov Jain(14/12/2025 12:57 AM IDT)
*Shah Jahan Ishaq(15/12/2025 1:56 AM IDT)
Joseph Shalom Liu(15/12/2025 8:39 PM IDT)
*Florian Sikora(16/12/2025 1:11 PM IDT)
Mathias Schenker(16/12/2025 5:23 PM IDT)
Jackson La Vallee(16/12/2025 10:49 PM IDT)
*John Tromp(17/12/2025 12:28 PM IDT)
*Yash kumar kasaudhan(17/12/2025 4:54 PM IDT)
*Ignasi Guillén(17/12/2025 7:31 PM IDT)
*Hakan Summakoğlu(17/12/2025 11:55 PM IDT)
Danyil Vorobiov(18/12/2025 7:40 PM IDT)
*Giovanni Basso(18/12/2025 9:48 PM IDT)
*Jean-François Hermant(19/12/2025 1:07 AM IDT)
*Robert Berec(19/12/2025 6:44 AM IDT)
Karl D’Souza(19/12/2025 5:54 PM IDT)
*Fabio Filatrella(20/12/2025 12:46 AM IDT)
*Alt Fresneda(20/12/2025 3:12 AM IDT)
*Thomas Klöckler(20/12/2025 4:43 PM IDT)
*Paul Upchurch(20/12/2025 9:29 PM IDT)
Ken Dsouza(22/12/2025 11:32 PM IDT)
*Tim Walters(23/12/2025 9:50 AM IDT)
Nagendra Gd(23/12/2025 10:19 PM IDT)
*Marios Zachariades(24/12/2025 6:58 AM IDT)
*Christofer Ohlsson(24/12/2025 10:34 AM IDT)
*Motty Porat(25/12/2025 4:35 PM IDT)
Paul Revenant(25/12/2025 10:47 PM IDT)
Stefan Wirth(26/12/2025 3:07 AM IDT)
*Balakrishnan V(27/12/2025 12:59 AM IDT)
*Fakih Karademir(27/12/2025 1:49 PM IDT)
*Gil Citro(27/12/2025 11:57 PM IDT)
*Daniel Lincke(28/12/2025 11:18 PM IDT)
Preetham Poluparthi(29/12/2025 9:52 AM IDT)
Kandala Savitha Viswanadh(29/12/2025 2:17 PM IDT)
*Franciraldo Cavalcante(29/12/2025 2:22 PM IDT)
*David Greer(29/12/2025 3:26 PM IDT)
Kandala Srinivas(30/12/2025 2:27 PM IDT)
*Evert van Dijken(30/12/2025 9:30 PM IDT)
*Oscar Volpatti(31/12/2025 4:19 AM IDT)
*Jan Fricke(31/12/2025 1:39 PM IDT)
Antti Syväniemi(2/1/2026 9:51 AM IDT)
Carlos Antonio Pinzón(2/1/2026 5:24 PM IDT)
*Karl Mahlburg(3/1/2026 4:30 AM IDT)
Marco Bellocchi(4/1/2026 1:50 AM IDT)