# Smallest prime number which when spelt out contains the letters P, R, I, M, E

So inspired by recent slew of questions based on prime numbers.

What is the smallest prime number when written out (Using the Western numbering system and English) would you encounter the letters P, R, I, M, E in that order. There can be any number and type of letters between them.

For example - one million and three is the smallest prime number where the letters M, A, T, H occur in that order.

Use the short scale only (that is, "1,000,000,000" is "one billion", not "one thousand million" or "one milliard"); you also may not use the less-common terms such as "dozen", "score", or "myriad", or Indian English terms such as "lakh" or "crore".

Disclaimer: I have not calculated this number myself due to its huge magnitude and lack of a list of primes that large

Hint below if you can't get started

The first instance of the letter p in a number is one septillion

• Presumably English only? (I've made an edit to that effect.) Sep 25, 2019 at 10:24
• May one use terms like "dozen" (12), "score" (20), "lakh" (Indian English, 100,000), "crore" (Indian English, 10,000,000), etc.? Sep 25, 2019 at 11:15
• @JeffZeitlin i specified the Western numbering system in the question, thus dozen, score and numbers from the Indian numbering system are not applicable Sep 25, 2019 at 11:16
• "Western numbering system" is undefined, or badly defined. If you wish to limit it to the English used in England and North America, then you implicitly allow "dozen" and "score", at the very least; recall a certain piece of U.S. oratory that began "Four Score and Seven...". Sep 25, 2019 at 11:18
• (Nota Bene: "Short scale" is what is used in the United States; 'one billion' is one thousand million. In "Long scale", 'one billion' is one million million; one thousand million is 'one milliard'.) Sep 25, 2019 at 11:26

First guess:

1000000000000000035000061
a.k.a. one sePtillion thiRty fIve Million and sixty onE

• N tbbq pnaqvqngr jbhyq unir orra bar frcgvyyvba, guvegl svir zvyyvba, naq guvegl-bar, ohg gung vf hasbeghangryl rdhny gb 997,573,923,793 gvzrf 1,002,431,976,367. Sep 26, 2019 at 2:02

It is kind of cheating but how about the Standard way to render a Mersenne prime:

two to the power of five minus one

• Not cheating, this is just an answer to a different question. Sep 25, 2019 at 17:40
• Cheating would be answering: The smallest PRIME :) Sep 26, 2019 at 11:02
• @P1storius Last time I checked, 2^5-1 = 31 was indeed prime ... Sep 26, 2019 at 13:27
• @collapsar no doubt about that! Was just making a joke about what a real cheated answer would look like ;) Sep 26, 2019 at 13:34
• @P1storius Oh my, so I didnt get it ... and I want to solve puzzles ... ;) Sep 26, 2019 at 13:35