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Digits of numbers (Posted on 2020-03-30) Difficulty: 2 of 5
Here is pi to 37 decimal places.

3.1415926535897932384626433832795028841...

It turns out that 31415926535897932384626433832795028841 is prime, but you would need a computer to figure that out. Here is e to 37 decimal places.

2.7182818284590452353602874713526624977...

The largest prime number that is a substring of these digits is 828182845904523536028747135266249. Of course, that would be hard to find without a computer. However, if I showed you the first 37 digits after the decimal point of (sqrt(3)-1)^(sqrt(2)-1), then you could easily find the largest prime number in those digits. You could do it in your head. How? What is the largest prime substring of the first 37 digits of (sqrt(3)-1)^(sqrt(2)-1)?

  Submitted by Math Man    
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Solution: (Hide)
Here is (sqrt(3)-1)^(sqrt(2)-1) to 37 decimal places.

0.8788022048554406482542450245650665224...

The largest prime number in these digits is 7. Any prime number with more than 1 digit must end in 1, 3, 7, or 9. The only 1, 3, 7, or 9 in these digits is the 7 that is 2 digits after the decimal point. However, 87=3*29, so there are no multi-digit primes in the first 37 digits of (sqrt(3)-1)^(sqrt(2)-1). Therefore, the largest prime in the digits is 7.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No Subjectlaxmee2020-12-13 02:00:54
Dancing numberslaxmee2020-08-22 23:10:51
countingHappy Space2020-05-10 03:09:51
SolutionsolutionCharlie2020-03-30 21:12:59
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