June 2019 - Challenge

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Let's define a *smooth* number as a natural number with prime factors that are single-digit (less than 10).
An example of such a number is 1560674304, which is related (how?) to the 108th birthday of IBM.

This month's challenge is to find two sets of smooth numbers whose square root sums are close to each other.
For example, the sets \{2,6\} and \{15\} yield a distance between their square root sums of less than 0.01 since \sqrt{2}+\sqrt{6} = 3.86 \ldots \approx 3.87\ldots = \sqrt{15}.

Two sets that meet our criterion even better are \{2,10,15\}$ and $\{6,36\}, which yield an even smaller distance between their square root sums: \sqrt{2}+\sqrt{10}+\sqrt{15} = 8.44947\ldots \approx 8.44948\ldots = \sqrt{6}+\sqrt{36}.

Find two sets of smooth numbers that produce a distance d where 0 < d < 10^{-15}.



Bonus question: Find a smooth number that is connected to last month's bonus question (a date in May 2019).




Update (3/6): Hint for the bonus: Unix time.


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: 29/05/2019 @ 12:00 PM EST
Solution: 03/07/2019 @ 12:00 PM EST
List Updated: 03/07/2019 @ 12:00 PM EST

People who answered correctly:

Oleg Vlasii (29/05/2019 07:43 PM IDT)
Uoti Urpala (29/05/2019 08:50 PM IDT)
*Bert Dobbelaere (29/05/2019 10:57 PM IDT)
Reiner Martin (30/05/2019 11:45 AM IDT)
Thomas Huet (30/05/2019 02:01 PM IDT)
*Alper Halbutogullari (30/05/2019 08:55 PM IDT)
Lorenz Reichel (30/05/2019 09:33 PM IDT)
Jingran Lin (31/05/2019 12:48 AM IDT)
Anders Kaseorg (31/05/2019 04:49 AM IDT)
*Eden Saig (01/06/2019 02:48 AM IDT)
*Florian Fischer (01/06/2019 02:19 PM IDT)
Joseph DeVincentis (01/06/2019 07:32 PM IDT)
Andreas Stiller (02/06/2019 03:08 AM IDT)
Guenter Nowak (02/06/2019 10:34 AM IDT)
Boris Silantev (02/06/2019 03:16 PM IDT)
Alex Fleischer (03/06/2019 02:40 PM IDT)
Richard Gosiorovsky (03/06/2019 05:21 PM IDT)
Liubing Yu (04/06/2019 06:18 AM IDT)
Harald Bögeholz (04/06/2019 04:28 PM IDT)
John Tromp (04/06/2019 04:29 PM IDT)
Deron Stewart (04/06/2019 07:04 PM IDT)
Todd Will (04/06/2019 07:15 PM IDT)
*Haye Chan (05/06/2019 10:00 AM IDT)
IDT)
George Wahid (05/06/2019 05:38 PM IDT)
Michael van Fondern (05/06/2019 08:38 PM IDT)
Tom Chen (06/06/2019 07:06 AM IDT)
Richard Gosiorovsky (06/06/2019 02:08 PM IDT)
Albert Stadler (07/06/2019 12:02 AM IDT)
Lachezar Hristov (07/06/2019 03:01 PM IDT)
*Kang Jin Cho (07/06/2019 06:46 PM IDT)
Klaus Hoffmann (07/06/2019 07:28 PM IDT)
Vladimir Volevich (07/06/2019 10:33 PM IDT)
Rashid Naimi (08/06/2019 04:01 AM IDT)
JJ Rabeyrin (08/06/2019 02:35 PM IDT)
Klaus Hoffmann (08/06/2019 07:27 PM IDT)
Jacoby Jaeger (09/06/2019 01:27 AM IDT)
Noam Lasry (09/06/2019 05:36 PM IDT)
Xiao Liu (10/06/2019 09:02 AM IDT)
Johan Van Mengsel (10/06/2019 09:18 AM IDT)
Loukas Sidiropoulos (10/06/2019 11:53 PM IDT)
*Daniel Chong Jyh Tar (11/06/2019 10:31 AM IDT)
Yasodhar Patnaik (11/06/2019 06:53 PM IDT)
Robert Lang (12/06/2019 02:24 PM IDT)
Jan Fricke (12/06/2019 10:46 PM IDT)
Amos Guler (13/06/2019 10:27 AM IDT)
Amos Guler (13/06/2019 10:27 AM IDT)
Aaron Zolnai-Lucas (13/06/2019 06:51 PM IDT)
Dieter Beckerle (13/06/2019 11:44 PM IDT)
Daniel Bitin (14/06/2019 10:41 AM IDT)
Hermann Jurksch & Hugo Pfoertner (15/06/2019 01:54 AM IDT)
Pål Hermunn Johansen (16/06/2019 02:04 PM IDT)
*Miguel Sauam & Rogerio Ponce da Silva (21/06/2019 06:25 AM IDT)
*Chris Shannon (21/06/2019 12:11 PM IDT)
Gareth Ma (22/06/2019 11:39 AM IDT)
Charles Joscelyne (23/06/2019 10:04 PM IDT)
David Greer (24/06/2019 02:43 PM IDT)
Peter Gerritson (24/06/2019 10:32 PM IDT)
Kevin Naslund (25/06/2019 08:17 AM IDT)
Jimmy Waters (26/06/2019 07:08 PM IDT)
Muralidhar Seshadri (27/06/2019 09:53 AM IDT)
Calvin Pozderac (27/06/2019 05:08 PM IDT)
Chen Zixuan (29/06/2019 07:59 PM IDT)
Motty Porat (30/06/2019 05:53 PM IDT)
Radu-Alexandru Todor (01/07/2019 02:04 AM IDT)
Marco Bellocchi (02/07/2019 02:51 AM IDT)
*Li Li (02/07/2019 07:24 AM IDT)
Nyles Heise (02/07/2019 08:11 AM IDT)
Oscar Volpatti (03/07/2019 10:56 AM IDT)