Problems & Puzzles: Puzzles

Puzzle 1055. Google Prime Number Claudio Meller sent the following nice link, where it is stated: "379009, es el número primo de Google". The same has been stated by Earls this way in a curio: 379009 is A prime number that spells Google when turned upside down on a calculator. [Earls] Claudio's questions are: Q. Qué otras páginas, países, palabras, etc tienen está característica??

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Contributions came from Ivan Ianakiev, Emmanuel Vantieghem

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Ivan wrote:

For the replacement rule {"0" -> "o", "3" -> "e", "5" -> "s", "7" -> "l", "9" -> "g"} 

1. The English numbers/words are
{3,5,7,37,53,59,97,337,509,733,739,773,907,937,3907,5309,5507,35339,53507,55079,379009,379909}

{e,s,l,le,es,gs,lg,lee,gos,eel,gel,ell,log,leg,loge,goes,loss,geese,loses,gloss,google,goggle}

2. The Spanish numbers/words are
{3,37,53,73,307,337,353,373,709,739,37337,50773,53507,53773,5050709}

{"e", "le", "es", "el", "loe", "lee", "ese", "ele", "gol", "gel", "leele", "ellos", "loses", "elles", "golosos"}

3. My algorithm generates only the numbers that are prime and consisting of the digits {0,3,5,7,9} and checks whether the corresponding words are valid. Another possible approach is to convert every word in the dictionary into a number and check whether it is prime and consisting of the digits mentioned, but I think it will take a lot of time and effort to check every single word in the dictionary.
 

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Emmanuel wrote:

If I understood well (which is probably not the case due to my very restricted knowledge of Spanish), you are looking for prime numbers that, when put on the display of a calculator, one reads them as "readable" expressions when the calculator is "turned".

I found the following primes below 10^10 : 13, 17, 37, 53, 71, 73, 137, 149, 173, 307, 313, 317, 337, 353, 373, 379, 509, 709, 719, 733, 739, 773, 907, 919, 937, 3137, 3517, 3533, 3709, 3719, 3739, 3793, 3907, 3917, 4507, 4517, 4937, 5171, 5179, 5507, 7039, 7309, 7351, 7717, 17737, 31513, 31907, 34537, 34913, 35317, 35339, 35507, 35509, 35537, 37049, 37717, 39107, 39317, 39937, 45137, 45179, 51907, 55079, 57719, 73553, 77137, 317717, 371737, 379009, 379909, 451771, 577349, 739051, 3177149, 4519919, 553735009

that are "read" as :

ei, li, le, es, il, el, lei, ghi, eli, loe, eie, lie, lee, ese, ele, gle, gos, gol, gil, eel, gel, ell, log, gig, leg, leie, lise, eese, gole, gile, gele, egle, loge, lige, losh, lish, legh, ilis, glis, loss, geol, goel, isel, lill, lelli, eisie, logie, leshe, eighe, liese, geese, losse, gosse, lesse, ghole, lille, loige, liege, legge, leish, glish, logis, gloss, gills, essel, leill, lillie, lelile, google, goggle, illish, ghells, isogel, ghillie, giggish, gooseless.

Most words are not English (I could not find them in a dictionary), for instance : lille is a town in France, liege is a town in Belgium.  

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