Problems & Puzzles: Puzzles

Puzzle 143.  The first and the last five primes

Suppose you make a list in precise alphabetic order of all the prime numbers properly expressed in your native language (English, Spanish, French, etc.)

What are the first and the last five primes in such list in your language?

Hints?

In English "zero" is the last number (not prime)
In Spanish "catorce" is the first number (not prime)

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n.b. This puzzle is an extension of the one posted to me by my friend Jean Charles Meyrignac who asked (25/5/2001) just for the first and for the last prime in alphabetical order.

Solution

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Donald Knuth documents here http://historical.ncstrl.org/litesite-data/stan/CS-TR-81-863.pdf a seminar, held in autumn 1980, where students were given challenges including that of finding the alphabetically last prime. The seminar was in the USA so American English was used (101=one hundred one, not one hundred and one; 1000000000, not 1000000000000=one billion).

On page 20 he reports that it is:

"two vigintillion two undecillion two trillion two thousand two hundred ninety-three":

2,000,000,000,000,000,000,000,000,002,000,000,000,000,000,000,000,002,000,000,002,293

Who deserves credit? Many students: Knuth reports that many groups found the correct answer.

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As a matter of fact in this interesting document found by Sabey, it is also reported the first prime number (in English):

"eight billion eighteen million eighteen thousand eight hundred fifty-one": 8,018,018,851

As a curious note Knut wrote in this document that:

The problem of the first prime was raised by Edward R. Wolpow in Word Ways 13 (1980), 55-56, who said that it is "computationally impossible to determine the alphabetically last prime." We hope to prove him wrong.

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Claudio Meller wrote (May 2011):

Según la página de Rodolfo Kurchan

http://www.micolecciondejuegos.com.ar/2009/05/mi-coleccion-de-numeros-curiosos.html

14.014.014.014.159: Catorce billones catorce mil catorce millones catorce mil ciento cincuenta y nueve es el primer número primo en el diccionario (encontrado por Hilario Fernandez Long)

 

Basado en esto yo encontré los siguientes cuatro (gracias al addin):

 

1 -14014014014159

2 -14014014014149

3 -14014014014177

4 -14014014014173

5 -14014014014131

 

En letras :

Catorce billones catorce mil catorce millones catorce mil ciento cincuenta y nueve

Catorce billones catorce mil catorce millones catorce mil ciento cuarenta y nueve

Catorce billones catorce mil catorce millones catorce mil ciento setenta y siete

Catorce billones catorce mil catorce millones catorce mil ciento setenta y tres

Catorce billones catorce mil catorce millones catorce mil ciento treinta y uno

 

Para los últimos, es un poco mas complicado, para algunos existe el vigillón (10^120) entonces habría que buscar un primo de 120 digitos, si no tomamos en cuenta el vigillón, tomamos  los primos de 21 trillones

 

Entonces