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)

***

On Nov 9, 2025, Claudio Meller wrote:

 Te mando las soluciones que encontré en español e Inglés.

No Palabra Símbolos Químicos Pesos atómicos Número Primo Digitos
1   nacionalsindicalista  N-AC-I-O-N-AL-S-I-ND-I-C-AL-I-S-TA 7-89-53-8-7-13-16-53-60-53-6-13-53-16-73 78953871316536053613531673 26
2   psicoterapéuticas P-S-I-C-O-TE-RA-P-EU-TI-C-AS 15-16-53-6-8-52-88-15-63-22-6-33 151653685288156322633 21
3   prohibicionista PR-O-H-I-B-I-C-I-O-N-I-S-TA 59-8-1-53-5-53-6-53-8-7-53-16-73 59815355365387531673 20
4   hiperinflaciones H-I-P-ER-IN-FL-AC-I-O-N-ES 53-15-68-49-114-89-53-8-7-99 15315684911489538799 20
5   invertebraciones  I-N-V-ER-TE-BR-AC-I-O-N-ES 53-7-23-68-52-35-89-53-8-7-99 5372368523589538799 19
6   inversionista  I-N-V-ER-S-I-O-N-I-S-TA 53-7-23-68-16-53-8-7-53-16-73 5372368165387531673 19
7   inflacionísticas IN-F-LA-C-I-O-N-I-S-TI-C-AS  49-9-57-6-53-8-7-53-16-22-6-33 4995765387531622633 19
8   colaboracionista CO-LA-B-O-RA-C-I-O-N-I-S-TA 27-57-5-8-88-6-53-8-7-53-16-73 2757588865387531673 19
9   viceprovincias V-I-CE-PR-O-V-I-N-C-I-AS 23-53-58-59-8-23-53-7-6-53-33 2353585982353765333 19
10 subsistencias  S-U-B-S-I-S-TE-N-C-I-AS 16-92-5-16-53-16-52-7-6-53-33 1692516531652765333 19
  Con verbos conjugados        
1 nacionalsindicalista N-AC-I-O-N-AL-S-I-ND-I-C-AL-I-S-TA 7-89-53-8-7-13-16-53-60-53-6-13-53-16-73 78953871316536053613531673 26
2   internacionalicémosela IN-TE-RN-AC-I-O-N-AL-I-CE-MO-SE-LA  49-52-86-89-53-8-7-13-53-58-42-34-57 495286895387135358423457 24
3   intensificándonosla IN-TE-N-S-I-F-I-CA-ND-O-NO-S-LA 49-52-7-16-53-9-53-20-60-8-102-16-57 495271653953206081021657 24
4   intensificándoosla I-N-TE-N-S-I-F-I-CA-ND-O-O-S-LA 53-7-52-7-16-53-9-53-20-60-8-8-16-57 53752716539532060881657 23
5   precipitándonosla  P-RE-C-I-P-I-TA-ND-O-NO-S-LA 15-75-6-53-15-53-73-60-8-102-16-5 15756531553736081021657 23
6   personificárnosla P-ER-S-O-N-I-F-I-C-AR-NO-S-LA 15-68-16-8-7-53-9-53-6-18-102-16-57 15681687539536181021657 23
7   escenificándonosla ES-CE-N-I-F-I-CA-ND-O-NO-S-LA 99-58-7-53-9-53-20-60-8-102-16-57 9958753953206081021657 22
8   biopsicosociales B-I-O-P-S-I-C-O-S-O-C-I-AL-ES 5-53-8-15-16-53-6-8-16-8-6-53-13-99 5538151653681686531399 22
9  interaccionándoosla I-N-TE-RA-C-C-I-O-NA-ND-O-O-S-LA 53-7-52-88-6-6-53-8-11-60-8-8-16-57 5375288665381160881657 22
10  internacionalícensela I-N-TE-RN-AC-I-O-NA-LI-CE-N-SE-LA 53-7-52-86-89-53-8-11-3-58-7-34-57 5375286895381135873457 22
  Inglés        
1   professionalisation  PR-O-F-ES-SI-O-N-AL-I-S-AT-I-O-N 59-8-9-99-14-8-7-13-53-16-85-53-8-7 5989991487135316855387 22
2   percussionists  P-ER-C-U-S-S-I-O-N-I-S-TS 15-68-6-92-16-16-53-8-7-53-16-117 1568692161653875316117 22
3   ophthalmoscopical O-P-H-TH-AL-MO-S-C-O-P-I-C-AL 8-15-1-90-13-42-16-6-8-15-53-6-13 815190134216681553613 21
4   prosopographical PR-O-S-O-P-OG-RA-P-H-I-C-AL 59-8-16-8-15-118-88-15-1-53-6-13 598168151188815153613 21
5   progressionists PR-OG-RE-S-S-I-O-NI-S-TS 59-118-75-16-16-53-8-28-16-117 591187516165382816117 21
6   internationalises I-N-TE-RN-AT-I-O-N-AL-I-S-ES 53-7-52-86-85-53-8-7-13-53-16-99 537528685538713531699 21
7   psychophysical P-S-Y-C-HO-P-H-Y-S-I-C-AL 15-16-39-6-67-15-1-39-16-53-6-13 151639667151391653613 21
8   biophysicists BI-O-P-H-Y-S-I-C-I-S-TS 83-8-15-1-39-16-53-6-53-16-117 83815139165365316117 20
9   geophysicists GE-O-P-H-Y-S-I-C-I-S-TS  32-8-15-1-39-16-53-6-53-16-117 32815139165365316117 20
10  perfusionists  P-ER-F-U-S-I-O-N-I-S-TS 15-68-9-92-16-53-8-7-53-16-117 15689921653875316117 20

***

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