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The next term (a(4)) has 242 digits. - Harvey P. Dale, Sep 13 2021
Module[{nn=500, l10}, l10=RealDigits[Log[10], 10, nn][[1]]; Select[ Table[ FromDigits[ Take[l10, n]], {n, nn}], PrimeQ]] (* Harvey P. Dale, Sep 13 2021 *)
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Eric W. Weisstein, <a href="/A228241/b228241.txt">Table of n, a(n) for n = 1..75</a>
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Eric W. Weisstein, <a href="/A228241/b228241_1.txt">Table of n, a(n) for n = 1..7</a>
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Eric W. Weisstein, <a href="/A228241/b228241_1.txt">Table of n, a(n) for n = 1..57</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConstantPrimes.html"> Constant Primes</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NaturalLogarithmof10Digits.html">Natural Logarithm of 10 Digits</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NaturalLogarithmof10Digits.html">Natural Logarithm of 10 Digits</a>
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