Problems & Puzzles: Puzzles

Puzzle 1210 Prime Atomic Words  

On Feb 25, 2025, Michael Branicky invited me to see the page of Puzzles Corner https://www.technologyreview.com/2025/02/25/1111905/puzzle-corner-70/ , that this month is edited by himself.

After a short revisión of the four puzzles composed for this edition, I was interested specifically the third one one, named M/A3:

"Each element in the periodic table has a one- or two-letter symbol: H for hydrogen, He for helium, etc.

Call an English word 'molecular' if it can be spelled
completely using chemical symbols, with case ignored.

For example, FUN, TeCHNICAl, VISiONArY, and SeArCHEs are
molecular words.

What is the longest molecular word you can find?
"

With little effort I devised how to turn this puzzle into a prime numbers puzzle:

After you get a Molecular Word (I prefer the name "Atomic Words), IN YOUR NATIVE LANGUAGE, put the atomic number instead of each one of the 118 possible chemical elements, concatenate these atomic numbers and calculate if the resuting concatenated number is a prime number or not.

Examples:

Ex.1.a
Word in Spanish: "Interacción"
Chemical symbols: "In-Te-Ra-C-C-I O-N"
Atomic numbers: "49-52-88-6-6-53-8-7"
Prime number: "495288665387" (12 digits)

Ex.1.b
Word in Spanish: "Interacción"
Chemical symbols: "I-N-Te-Ra-C-C-I O-N"
Atomic numbers: "53-7-52-88-6-6-53-8-7"
Prime number: "5375288665387" (13 digits)


(Notice that this spanish word accepts two ways of spelling using chemical elements, both producing two distinct prime numbers)


Ex. 2
Word in English:"Calculation"
Chemcial symbols:"C-Al-C-U-La-Ti-O-N"
Atomic numbers:"6-13-6-92-57-22-8-7"
Prime number: 613692572287 (12 digits)

(This last example was provided by Michael Branicky, short after I explained my puzzle-extension to him)

Q1. Send the largest prime number you can find, obtained by the above procedure, using only (one) words in your own native language.

Q2. Send the largest multiple prime numbers you can find, obtained by the above procedure, using only (one) words in your own native language,


Note1: Please use only valid words, according to the dictionary authorities in your language.
For Spanish use this on line dictionary: https://dle.rae.es/
For English use this on line dictionary: https://www.oed.com/

Note2: For your trial & error search, perhaps you will find useful these links: https://www.chemspeller.com/
or https://periodictable.chemicalaid.com/fun/spell-words-with-elements.php? or https://blendertimer.com/web-tools/periodic-table-word-finder

The last two ones links produce (sometimes) all the different ways of spelling possible for the same word.

Note3: This puzzle is a kind of follow-up of the puzzles 693, 1070 & 1071, of my site.


From Feb. 1-7, 2025, contributions came from Ivan Ianakev, Michael Branicky, Michael Hürter

rter

***

Ivan wrote:

NONOCCUPATIONAL has 3 different prime representations:

Chemical symbols:"No - No - C - C - U - Pa - Ti - O - N - Al"
Atomic numbers:"102-102-6-6-92-91-22-8-7-13"
Prime number: 102102669291228713 (18 digits)

Chemical symbols:"N - O - No - C - C - U - Pa - Ti - O - N - Al"
Atomic numbers:"7-8-102-6-6-92-91-22-8-7-13"
Prime number: 78102669291228713 (17 digits)

 

Chemical symbols:"N - O - No - C - Cu - Pa - Ti - O - N - Al"
Atomic numbers:"7-8-102-6-29-91-22-8-7-13"
Prime number: 7810262991228713 (16 digits)


(Unfortunately this word is not accepted by OED, but it was accepted by Merriam Webster Dictionary, so I´m going to accept it. CR)


Later Ivan wrote again:


Word in English:"supererogation", accepted by OED.

Chemical symbols:"S-U- P-Er-Er-Og-At-I-O-N"
Atomic numbers:"16-92-15-68-68-118-85-53-8-7"
Prime number: 1692156868118855387 (19 digits)

***

Michael Branicky wrote:

Q1
"PHOSPHOMONOESTERASES" => "P-HO-S-P-H-O-MO-NO-ES-TE-RA-S-ES" => "15-67-16-15-1-8-42-102-99-52-88-16-99" => 1567161518421029952881699 (25 digits)

Q2

2 ways:
"INACCESSIBILITIES" => "I-N-AC-C-ES-S-I-B-I-LI-TI-ES" => "53-7-89-6-99-16-53-5-53-3-22-99" => 53789699165355332299 (20 digits)
"INACCESSIBILITIES" => "IN-AC-CE-S-SI-BI-LI-TI-ES"    => "49-89-58-16-14-83-3-22-99"       =>    49895816148332299 (17 digits)

3 ways:
"INCONSISTENTLY" => "IN-CO-N-S-I-S-TE-N-TL-Y"  => "49-27-7-16-53-16-52-7-81-39" => 492771653165278139 (18 digits)
"INCONSISTENTLY" => "I-N-C-O-N-SI-S-TE-N-TL-Y" => "53-7-6-8-7-14-16-52-7-81-39" =>  53768714165278139 (17 digits)
"INCONSISTENTLY" => "IN-CO-N-SI-S-TE-N-TL-Y"   => "49-27-7-14-16-52-7-81-39"    =>   4927714165278139 (16 digits)

4 ways:
"KINNIKINNICK" => "K-I-N-N-I-K-IN-N-I-C-K" => "19-53-7-7-53-19-49-7-53-6-19" => 195377531949753619 (18 digits)
"KINNIKINNICK" => "K-IN-N-I-K-I-N-N-I-C-K" => "19-49-7-53-19-53-7-7-53-6-19" => 194975319537753619 (18 digits)
"KINNIKINNICK" => "K-IN-N-I-K-IN-N-I-C-K"  => "19-49-7-53-19-49-7-53-6-19"   =>  19497531949753619 (17 digits)
"KINNIKINNICK" => "K-IN-NI-K-I-N-N-I-C-K"  => "19-49-28-19-53-7-7-53-6-19"   =>  19492819537753619 (17 digits)

(All of these four words are accepted by OED. CR)

***

Michael Hürter wrote:

I found the following german words for Puzzle 1210:
 
Q1:
 
geschichtsrevisionistisches
ge s c h i c h ts re v i s i o n i s ti sc h es
32 16 6 1 53 6 1 117 75 23 53 16 53 8 7 53 16 22 21 1 99
321661536111775235316538753162221199 (36 digits)
 
Q2:
 
linksnationalistisches
li n k s n at i o n al i s ti sc h es
3 7 19 16 7 85 53 8 7 13 53 16 22 21 1 99
37191678553871353162221199 (26 digits)
 
linksnationalistisches
li n k s na ti o na li s ti s c h es 
3 7 19 16 11 22 8 11 3 16 22 16 6 1 99
371916112281131622166199 (24 digits)

***

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