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%I #62 Sep 08 2022 08:45:35
%S 23,67,89,199,331,353,397,419,463,617,661,683,727,859,881,947,991,
%T 1013,1123,1277,1321,1409,1453,1607,1783,1871,2003,2069,2113,2179,
%U 2267,2311,2333,2377,2399,2531,2663,2707,2729,2861,2927,2971,3037,3169,3191,3257
%N Primes congruent to 1 mod 11.
%C Conjecture: Also primes p such that ((x+1)^11-1)/x has 10 distinct irreducible factors of degree 1 over GF(p). - _Federico Provvedi_, Apr 17 2018
%H Vincenzo Librandi, <a href="/A141849/b141849.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ 10n log n. - _Charles R Greathouse IV_, Jul 02 2016
%p a:=select(n->isprime(n) and modp(n,11)=1,[$1..4000]); # _Muniru A Asiru_, Apr 19 2018
%t Select[Range[1,10000,11],PrimeQ] (* _Vladimir Joseph Stephan Orlovsky_, May 18 2011 *)
%o (Magma) [ p: p in PrimesUpTo(5000) | p mod 11 eq 1 ]; // _Vincenzo Librandi_, Apr 19 2011
%o (PARI) is(n)=isprime(n) && n%11==1 \\ _Charles R Greathouse IV_, Jul 01 2016
%o (PARI) forstep(n=2, 1e3, 2, if(isprime(p=11*n+1), print1(p, ", "))); \\ _Altug Alkan_, Apr 19 2018
%o (GAP) Filtered([1..4000],n->n mod 11=1 and IsPrime(n)); # _Muniru A Asiru_, Apr 19 2018
%Y Cf. A000040, A090187, A102656.
%Y Prime sequences A# (k,r) of the form k*n+r with 0 <= r <= k-1 (i.e., primes == r (mod k), or primes p with p mod k = r) and gcd(r,k)=1: A000040 (1,0), A065091 (2,1), A002476 (3,1), A003627 (3,2), A002144 (4,1), A002145 (4,3), A030430 (5,1), A045380 (5,2), A030431 (5,3), A030433 (5,4), A002476 (6,1), A007528 (6,5), A140444 (7,1), A045392 (7,2), A045437 (7,3), A045471 (7,4), A045458 (7,5), A045473 (7,6), A007519 (8,1), A007520 (8,3), A007521 (8,5), A007522 (8,7), A061237 (9,1), A061238 (9,2), A061239 (9,4), A061240 (9,5), A061241 (9,7), A061242 (9,8), A030430 (10,1), A030431 (10,3), A030432 (10,7), A030433 (10,9), this sequence (11,1), A090187 (11,2), A141850 (11,3), A141851 (11,4), A141852 (11,5), A141853 (11,6), A141854 (11,7), A141855 (11,8), A141856 (11,9), A141857 (11,10), A068228 (12,1), A040117 (12,5), A068229 (12,7), A068231 (12,11).
%Y Cf. A034694 (smallest prime == 1 (mod n)).
%Y Cf. A038700 (smallest prime == n-1 (mod n)).
%Y Cf. A038026 (largest possible value of smallest prime == r (mod n)).
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Jul 11 2008