{"id":17282,"date":"2026-03-16T11:14:38","date_gmt":"2026-03-16T15:14:38","guid":{"rendered":"https:\/\/blogs.mathworks.com\/pick\/?p=17282"},"modified":"2026-04-01T13:04:45","modified_gmt":"2026-04-01T17:04:45","slug":"matlab-user-john-derrico-finds-largest-known-reversible-prime-with-12346-digits","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/pick\/2026\/03\/16\/matlab-user-john-derrico-finds-largest-known-reversible-prime-with-12346-digits\/","title":{"rendered":"MATLAB user John D’Errico finds largest known reversible prime with 12,346 digits"},"content":{"rendered":"
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Mike's pick this week is a candidate for the new world-record reversible prime number<\/a> found by John D'Errico<\/a>.<\/div>\r\n
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<\/div>\r\n
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isprime([13 31])<\/span><\/div>\r\n
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ans = <\/span>1\u00d72 logical array<\/span><\/div>\r\n<\/div>\r\n
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1 1<\/div>\r\n
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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<\/a> recently discussed the discovery of the (then) largest known emirp. It had 10,002 decimal digits. Wikipedia currently lists 117,954,861 \u00d7 1011,111 + 1 as the largest known emirp with which has 11,120 digits.<\/div>\r\n

How MATLAB user, John D'Errico, found a 12,346 digit emirp<\/h2>\r\n
The short version of the story is that John looked for emirps of the form 10^n + a and used symbolic toolbox<\/a> and parallel computing toolbox<\/a> 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<\/span> 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).<\/div>\r\n
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.<\/a> 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!<\/div>\r\n
We fully expect, and hope, that this record will not stand for long. Happy hunting!<\/div>\r\n
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