Find all positive integers $n$ and prime $p$ such that
$$10^n+1=p$$
2026-03-27 21:35:50.1774647350
A prime number of the form $10^n+1$
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Probably , the only primes of the form $$10^n+1$$ are $2,11$ and $101$. If there is another such prime, the exponent must be a power of $2$ and exceed $10^6$
Look at this site for factors and the current status :
http://factordb.com/index.php?query=10%5E2%5En%2B1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=20&format=1&sent=Show