Problems & Puzzles: Puzzles

 Puzzle 658 Find primes such that... Reading a notice reported in the site "Mathpuzzle" by Ed Pegg Jr., I have developed the following two prime versions of an extremely nice puzzle original by Eric Harshbarger that originally deals not wit prime numbers: Q1. (the easy version) What is the smallest prime number that has one of one digit, two of another digit, three of another digit, ..., and ten of another digit?. Redo this for the largest prime. Q2. (the difficult version) What is the smallest spelled-out prime number that has one of one letter, two of another letter, three of another letter, ..., and ten of another letter? Notes 1) You are able to send solutions to Q2 for your native language. 2) If you send a solution to Q2 for your X-native language, please use the current standard practice in this X language to name billions, trillions, etc.. That is to say, use the appropriate/typical short/long scale notation for this X-language. 3) Please notice that in our two questions we ask for a maximum of ten, not nine, digits or letters, while Eric ask for for a maximum of nine letters.

Contributions came from Giovanni Resta and Emmanuel Vantieghem.

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Both sent for Q1:

1000000000011111111222222223333333444444555556666789977 and
9999999999888888888777777776666666555555444443333110221

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Carlos Rivera wrote:

In Spanish I found this prime as the smallest with an increasing quantity of letters from 1 to 11:

1326605911

"mil trescientos veintiseis millones seiscientos cinco mil, novecientos once"

r=1, v=2, m=3, l=4, t=5, c=6, o=7, n=8, s=9, e=10, i=11

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