

A045707


Primes with first digit 1.


27



11, 13, 17, 19, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151
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OFFSET

1,1


COMMENTS

Also primes with all divisors starting with digit 1. Complement of A206288 (nonprime numbers with all divisors starting with digit 1) with respect to A206287 (numbers with all divisors starting with digit 1).  Jaroslav Krizek, Mar 04 2012
Cohen and Katz show that the set of primes with first digit 1 has no natural density, but has supernatural/Dirichlet density log_{10} (2) ~= 0.3, the primes with first digit 2 have (supernatural) density log_{10} (3/2) ~= 0.176, ... and the primes with first digit 9 have density log_{10} (10/9) ~= 0.046. This would seem to explain the first digit phenomenon. Note that sum_{k = 1}^9 log_{10} (k+1)/k = 1.  Gary McGuire, Dec 22 2004


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Daniel I. A. Cohen and Talbot M. Katz, Prime numbers and the first digit phenomenon, J. Number Theory 18 (1984), 261268.


MATHEMATICA

Select[Table[Prime[n], {n, 500}], First[IntegerDigits[#]] == 1 &]
Flatten[Table[Prime[Range[PrimePi[10^n] + 1, PrimePi[2 * 10^n]]], {n, 3}]] (* Alonso del Arte, Jul 18 2014 *)


PROG

(MAGMA) [p: p in PrimesUpTo(10^4)  IsOne(Intseq(p)[#Intseq(p)])]; // Bruno Berselli, Jul 19 2014


CROSSREFS

For primes with initial digit d (1 <= d <= 9) see A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715; A073517, A073516, A073515, A073514, A073513, A073512, A073511, A073510, A073509
Column k=1 of A262369.
Sequence in context: A068492 A206287 A306661 * A032591 A088265 A327348
Adjacent sequences: A045704 A045705 A045706 * A045708 A045709 A045710


KEYWORD

nonn,base


AUTHOR

Felice Russo


EXTENSIONS

More terms from Erich Friedman.
CohenKatz reference from Victor S. Miller, Dec 21 2004


STATUS

approved



