MATLAB user John D’Errico finds largest known reversible prime with 12,346 digits
Mike's pick this week is a candidate for the new world-record reversible prime number found by John D'Errico.
A reversible prime, (also known as an emirp), is a prime number that yields a different prime when its digits are reversed. An example is 13. Reversing this gives 31 and both are prime
isprime([13 31])
Checking if small numbers are emirp is relatively straightforward but things get rather more complex when we start looking at larger numbers. Matt Parker's Numberphile recently discussed the discovery of the (then) largest known emirp. It had 10,002 decimal digits. Wikipedia currently lists 117,954,861 × 1011,111 + 1 as the largest known emirp with which has 11,120 digits.
How MATLAB user, John D'Errico, found a 12,346 digit emirp
The short version of the story is that John looked for emirps of the form 10^n + a and used symbolic toolbox and parallel computing toolbox to make use of all 16 cores on his desktop computer to burn through the search space. The result is that he found that 10^12338*79191501 + 1 is a 12,346 digit emirp, currently the largest known (although I'd prefer us to get independent verification before we suggest an update the Wikipedia page).
Why he chose that particular form of emirp, all of this code and full discussion of his journey can be found in this MATLAB discussion thread. I found it fascinating to follow him on his journey from 'This is a promising candidate' to 'We can say that it's highly probable that this is an emirp' to 'This is definitely an emirp'! Great work John!
We fully expect, and hope, that this record will not stand for long. Happy hunting!
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See Also
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Prime Spiral
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Prime Spiral #2
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