A030459 -id:A030459 - cp's OEIS frontend

A001359 Lesser of twin primes.

3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607

Offset: 1

N. J. A. Sloane

Also, solutions to phi(n + 2) = sigma(n). - Conjectured by Jud McCranie, Jan 03 2001; proved by Reinhard Zumkeller, Dec 05 2002
The set of primes for which the weight as defined in A117078 is 3 gives this sequence except for the initial 3. - Rémi Eismann, Feb 15 2007
The set of lesser of twin primes larger than three is a proper subset of the set of primes of the form 3n - 1 (A003627). - Paul Muljadi, Jun 05 2008
It is conjectured that A113910(n+4) = a(n+2) for all n. - Creighton Dement, Jan 15 2009
I would like to conjecture that if f(x) is a series whose terms are x^n, where n represents the terms of sequence A001359, and if we inspect {f(x)}^5, the conjecture is that every term of the expansion, say a_n * x^n, where n is odd and at least equal to 15, has a_n >= 1. This is not true for {f(x)}^k, k = 1, 2, 3 or 4, but appears to be true for k >= 5. - Paul Bruckman (pbruckman(AT)hotmail.com), Feb 03 2009
A164292(a(n)) = 1; A010051(a(n) - 2) = 0 for n > 1. - Reinhard Zumkeller, Mar 29 2010
From Jonathan Sondow, May 22 2010: (Start)
About 15% of primes < 19000 are the lesser of twin primes. About 26% of Ramanujan primes A104272 < 19000 are the lesser of twin primes.
About 46% of primes < 19000 are Ramanujan primes. About 78% of the lesser of twin primes < 19000 are Ramanujan primes.
A reason for the jumps is in Section 7 of "Ramanujan primes and Bertrand's postulate" and in Section 4 of "Ramanujan Primes: Bounds, Runs, Twins, and Gaps". (End)
Primes generated by sequence A040976. - Odimar Fabeny, Jul 12 2010
Primes of the form 2*n - 3 with 2*n - 1 prime n > 2. Primes of the form (n^2 - (n-2)^2)/2 - 1 with (n^2 - (n-2)^2)/2 + 1 prime so sum of two consecutive odd numbers/2 - 1. - Pierre CAMI, Jan 02 2012
Conjecture: For any integers n >= m > 0, there are infinitely many integers b > a(n) such that the number Sum_{k=m..n} a(k)*b^(n-k) (i.e., (a(m), ..., a(n)) in base b) is prime; moreover, when m = 1 there is such an integer b < (n+6)^2. - Zhi-Wei Sun, Mar 26 2013
Except for the initial 3, all terms are congruent to 5 mod 6. One consequence of this is that no term of this sequence appears in A030459. - Alonso del Arte, May 11 2013
Aside from the first term, all terms have digital root 2, 5, or 8. - J. W. Helkenberg, Jul 24 2013
The sequence provides all solutions to the generalized Winkler conjecture (A051451) aside from all multiples of 6. Specifically, these solutions start from n = 3 as a(n) - 3. This gives 8, 14, 26, 38, 56, ... An example from the conjecture is solution 38 from twin prime pairs (3, 5), (41, 43). - Bill McEachen, May 16 2014
Conjecture: a(n)^(1/n) is a strictly decreasing function of n. Namely a(n+1)^(1/(n+1)) < a(n)^(1/n) for all n. This conjecture is true for all a(n) <= 1121784847637957. - Jahangeer Kholdi and Farideh Firoozbakht, Nov 21 2014
a(n) are the only primes, p(j), such that (p(j+m) - p(j)) divides (p(j+m) + p(j)) for some m > 0, where p(j) = A000040(j). For all such cases m=1. It is easy to prove, for j > 1, the only common factor of (p(j+m) - p(j)) and (p(j+m) + p(j)) is 2, and there are no common factors if j = 1. Thus, p(j) and p(j+m) are twin primes. Also see A067829 which includes the prime 3. - Richard R. Forberg, Mar 25 2015
Primes prime(k) such that prime(k)! == 1 (mod prime(k+1)) with the exception of prime(991) = 7841 and other unknown primes prime(k) for which (prime(k)+1)*(prime(k)+2)*...*(prime(k+1)-2) == 1 (mod prime(k+1)) where prime(k+1) - prime(k) > 2. - Thomas Ordowski and Robert Israel, Jul 16 2016
For the twin prime criterion of Clement see the link. In Ribenboim, pp. 259-260 a more detailed proof is given. - Wolfdieter Lang, Oct 11 2017
Conjecture: Half of the twin prime pairs can be expressed as 8n + M where M > 8n and each value of M is a distinct composite integer with no more than two prime factors. For example, when n=1, M=21 as 8 + 21 = 29, the lesser of a twin prime pair. - Martin Michael Musatov, Dec 14 2017
For a discussion of bias in the distribution of twin primes, see my article on the Vixra web site. - Waldemar Puszkarz, May 08 2018
Since 2^p == 2 (mod p) (Fermat's little theorem), these are primes p such that 2^p == q (mod p), where q is the next prime after p. - Thomas Ordowski, Oct 29 2019, edited by M. F. Hasler, Nov 14 2019
The yet unproved "Twin Prime Conjecture" states that this sequence is infinite. - M. F. Hasler, Nov 14 2019
Lesser of the twin primes are the set of elements that occur in both A162566, A275697. Proof: A prime p will only have integer solutions to both (p+1)/g(p) and (p-1)/g(p) when p is the lesser of a twin prime, where g(p) is the gap between p and the next prime, because gcd(p+1,p-1) = 2. - Ryan Bresler, Feb 14 2021
From Lorenzo Sauras Altuzarra, Dec 21 2021: (Start)
J. A. Hervás Contreras observed the subsequence 11, 311, 18311, 1518311, 421518311... (see the links), which led me to conjecture the following statements.
I. If i is an integer greater than 2, then there exist positive integers j and k such that a(j) equals the concatenation of 3k and a(i).
II. If k is a positive integer, then there exist positive integers i and j such that a(j) equals the concatenation of 3k and a(i).
III. If i, j, and r are positive integers such that i > 2 and a(j) equals the concatenation of r and a(i), then 3 divides r. (End)

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §3.2 Prime Numbers, p. 81.
Paulo Ribenboim, The New Book of Prime Number Records, Springer-Verlag NY 1996, pp. 259-260.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 192-197.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 111-112.

Chris K. Caldwell, Table of n, a(n) for n = 1..100000
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Abhinav Aggarwal, Zekun Xu, Oluwaseyi Feyisetan, and Nathanael Teissier, On Primes, Log-Loss Scores and (No) Privacy, arXiv:2009.08559 [cs.LG], 2020.
Chris K. Caldwell, First 100000 Twin Primes
Chris K. Caldwell, Twin Primes
Chris K. Caldwell, Largest known twin primes
Chris K. Caldwell, Twin primes
Chris K. Caldwell, The prime pages
P. A. Clement, Congruences for sets of primes, American Mathematical Monthly, vol. 56,1 (1949), 23-25.
Harvey Dubner, Twin Prime Statistics, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.2.
Andrew Granville and Greg Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004; Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
José Antonio Hervás Contreras, ¿Nueva propiedad de los primos gemelos?
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Thomas R. Nicely, Enumeration to 10^14 of the twin primes and Brun's constant, Virginia Journal of Science, 46:3 (Fall, 1995), 195-204.
Thomas R. Nicely, Enumeration to 10^14 of the twin primes and Brun's constant [Local copy, pdf only]
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Waldemar Puszkarz, Statistical Bias in the Distribution of Prime Pairs and Isolated Primes, vixra:1804.0416 (2018).
Fred Richman, Generating primes by the sieve of Eratosthenes
Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
P. Shiu, A Diophantine Property Associated with Prime Twins, Experimental mathematics 14 (1) (2005).
Jonathan Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-2010; Amer. Math. Monthly, 116 (2009) 630-635.
Jonathan Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.
Jonathan Sondow and Emmanuel Tsukerman, The p-adic order of power sums, the Erdos-Moser equation, and Bernoulli numbers, arXiv:1401.0322 [math.NT], 2014; see section 4.
Terence Tao, Obstructions to uniformity and arithmetic patterns in the primes, arXiv:math/0505402 [math.NT], 2005.
Apoloniusz Tyszka, On sets X subset of N for which we know an algorithm that computes a threshold number t(X) in N such that X is infinite if and only if X contains an element greater than t(X), 2019.
Eric Weisstein's World of Mathematics, Twin Primes
Index entries for primes, gaps between

Subsequence of A003627.
Cf. A001223, A006512 (greater of twin primes), A014574, A001097, A077800, A002822, A040040, A054735, A067829, A082496, A088328, A117078, A117563, A074822, A071538, A007508, A146214, A350246, A350247.
Cf. A104272 (Ramanujan primes), A178127 (lesser of twin Ramanujan primes), A178128 (lesser of twin primes if it is a Ramanujan prime).
Cf. A010051, A000040.

a001359 n = a001359_list !! (n-1)
a001359_list = filter ((== 1) . a010051' . (+ 2)) a000040_list
-- Reinhard Zumkeller, Feb 10 2015

[n: n in PrimesUpTo(1610) | IsPrime(n+2)];  // Bruno Berselli, Feb 28 2011

select(k->isprime(k+2),select(isprime,[$1..1616])); # Peter Luschny, Jul 21 2009
A001359 := proc(n)
   option remember;
   if n = 1
      then 3;
   else
      p := nextprime(procname(n-1)) ;
      while not isprime(p+2) do
         p := nextprime(p) ;
      end do:
      p ;
   end if;
end proc: # R. J. Mathar, Sep 03 2011

Select[Prime[Range[253]], PrimeQ[# + 2] &] (* Robert G. Wilson v, Jun 09 2005 *)
a[n_] := a[n] = (p = NextPrime[a[n - 1]]; While[!PrimeQ[p + 2], p = NextPrime[p]]; p); a[1] = 3; Table[a[n], {n, 51}]  (* Jean-François Alcover, Dec 13 2011, after R. J. Mathar *)
nextLesserTwinPrime[p_Integer] := Block[{q = p + 2}, While[NextPrime@ q - q > 2, q = NextPrime@ q]; q]; NestList[nextLesserTwinPrime@# &, 3, 50] (* Robert G. Wilson v, May 20 2014 *)
Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]]==2&][[All,1]] (* Harvey P. Dale, Jan 04 2021 *)
q = Drop[Prepend[p = Prime[Range[100]], 2], -1];
Flatten[q[[#]] & /@ Position[p - q, 2]] (* Horst H. Manninger, Mar 28 2021 *)

A001359(n,p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0,); p-2}
/* The following gives a reasonably good estimate for any value of n from 1 to infinity; compare to A146214. */
A001359est(n) = solve( x=1,5*n^2/log(n+1), 1.320323631693739*intnum(t=2.02,x+1/x,1/log(t)^2)-log(x) +.5 - n)
/* The constant is A114907; the expression in front of +.5 is an estimate for A071538(x) */ \\  M. F. Hasler, Dec 10 2008

from sympy import primerange, isprime
print([n for n in primerange(1, 2001) if isprime(n + 2)]) # Indranil Ghosh, Jul 20 2017

a(n) = A077800(2n-1).
A001359 = { n | A071538(n-1) = A071538(n)-1 }; A071538(A001359(n)) = n. - M. F. Hasler, Dec 10 2008
A001359 = { prime(n) : A069830(n) = A087454(n) }. - Juri-Stepan Gerasimov, Aug 23 2011
a(n) = prime(A029707(n)). - R. J. Mathar, Feb 19 2017

A030461 Primes that are concatenations of two consecutive primes.

Original entry on oeis.org

23, 3137, 8389, 151157, 157163, 167173, 199211, 233239, 251257, 257263, 263269, 271277, 331337, 353359, 373379, 433439, 467479, 509521, 523541, 541547, 601607, 653659, 661673, 677683, 727733, 941947, 971977, 10131019

Offset: 1

Patrick De Geest

Any term in the sequence (apart from the first) must be a concatenation of consecutive primes differing by a multiple of 6. - Francis J. McDonnell, Jun 26 2005

			a(2) is 3137 because 31 and 37 are consecutive primes and after concatenation 3137 is also prime. - _Enoch Haga_, Sep 30 2007

Georg Fischer, Table of n, a(n) for n = 1..5720 [First 1000 terms from Zak Seidov]

Cf. A030459.
Cf. A185934, A185935.
Subsequence of A045533.

a030461 n = a030461_list !! (n-1)
a030461_list = filter ((== 1) . a010051') a045533_list
-- Reinhard Zumkeller, Apr 20 2012

[Seqint( Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)) ): n in [1..200 ]| IsPrime(Seqint( Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)) )) ]; // Marius A. Burtea, Mar 21 2019

conc:=proc(a,b) local bb: bb:=convert(b,base,10): 10^nops(bb)*a+b end: p:=proc(n) local w: w:=conc(ithprime(n),ithprime(n+1)): if isprime(w)=true then w else fi end: seq(p(n),n=1..250); # Emeric Deutsch

Select[Table[p=Prime[n]; FromDigits[Join[Flatten[IntegerDigits[{p,NextPrime[p]}]]]],{n,170}],PrimeQ] (* Jayanta Basu, May 16 2013 *)

{digits(n) = if(n==0,[0],u=[];while(n>0,d=divrem(n,10);n=d[1];u=concat(d[2],u));u)} {m=1185;p=2;while(pKlaus Brockhaus

o=2;forprime(p=3,1e4, isprime(eval(Str(o,o=p))) & print1(precprime(p-1),p",")) \\ M. F. Hasler, Feb 06 2011

A030461(n) = concat(A030459(n),A030460(n)) = A045533( A000720( A030459(n))). - M. F. Hasler, Feb 06 2011

Edited by N. J. A. Sloane, Apr 19 2009 at the suggestion of Zak Seidov

A086040 Prime p concatenated with next 4 primes is also prime.

Original entry on oeis.org

7, 47, 53, 67, 97, 101, 149, 401, 431, 479, 487, 757, 827, 887, 1061, 1171, 1409, 1429, 1543, 1721, 1789, 1811, 1889, 1987, 2099, 2113, 2137, 2273, 2689, 2719, 2857, 3203, 3571, 3613, 3623, 3761, 3853, 3917, 3929, 4007, 4217, 4441, 4943, 5039, 5209, 5281, 5449

Offset: 1

Chuck Seggelin, Jul 07 2003

			a(1) = 7 because 7, 11, 13, 17 and 19 concatenated together yield 711131719, which is prime.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A030459, A030468, A030472, A086041.

Select[Partition[Prime[Range[800]],5,1],PrimeQ[FromDigits[Flatten[IntegerDigits/@#]]]&][[;;,1]] (* Harvey P. Dale, May 25 2025 *)

from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    plst = [2, 3, 5, 7, 11]
    slst = list(map(str, plst))
    while True:
        if isprime(int("".join(slst))):
            yield plst[0]
        plst = plst[1:] + [nextprime(plst[-1])]
        slst = slst[1:] + [str(plst[-1])]
print(list(islice(agen(), 50))) # Michael S. Branicky, Jan 26 2023

Offset corrected by Arkadiusz Wesolowski, May 10 2012

a(15) and beyond from Michael S. Branicky, Jan 26 2023

A174031 The smallest integer k>0 such that the double-concatenation prime(n) // prime(n+1) // k is a prime number.

Original entry on oeis.org

3, 3, 1, 19, 1, 1, 1, 1, 1, 1, 9, 11, 11, 17, 3, 1, 1, 3, 11, 17, 21, 19, 1, 7, 37, 7, 23, 37, 7, 1, 7, 7, 7, 11, 7, 33, 29, 31, 1, 13, 11, 17, 7, 11, 11, 9, 9, 1, 7, 7, 1, 13, 11, 19, 67, 1, 13, 21, 49, 13, 13, 1, 1, 23, 1, 1, 29, 1, 29, 7

Offset: 1

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 06 2010

Leading zeros in k are not allowed.
All entries k are odd with final digit 1, 3, 7 or 9.
Dirichlet's prime number theorem for arithmetic progressions says that the sequence is infinite.
Conjecture: 1 appears infinitely often.

			n=1: 2//3//1 = 231 = 3 * 7 * 11 is not prime, so k<>1. 233 = prime(51), therefore 3 is the first entry.
n=2: 3//5//1 = 351 = 3^3 * 13 is not prime, so k <> 1, but 353 = prime(71), therefore 3 is the second entry.
n=30: 113//127//1 = 1131271 = prime(87976), so the 30th entry is 1.

Cf. A030461, A030459, A030469, A171154

read("transforms") ;
A174031 := proc(n) for e from 1 do if isprime(digcatL([ithprime(n),ithprime(n+1),e])) then return e ; end if; end do: end proc:

Entries checked; replaced variables by OEIS standard names - R. J. Mathar, Nov 17 2010

A030460 Previous prime concatenated with this prime p is a prime.

Original entry on oeis.org

3, 37, 89, 157, 163, 173, 211, 239, 257, 263, 269, 277, 337, 359, 379, 439, 479, 521, 541, 547, 607, 659, 673, 683, 733, 947, 977, 1019, 1039, 1187, 1193, 1213, 1229, 1277, 1373, 1459, 1471, 1663, 1693, 1721, 1747, 1867, 1979, 2081, 2179

Offset: 1

Patrick De Geest

Terms 157, 257, 263, 541, 1187, 1459, 2179 also belong to A030459. [Carmine Suriano, Jan 27 2011]

Harvey P. Dale, Table of n, a(n) for n = 1..10000 [extending M.F. Hasler's prior b-File beyond n=4110]

Transpose[Select[Partition[Prime[Range[400]],2,1], PrimeQ[FromDigits[ Flatten[IntegerDigits/@#]]]&]][[2]] (* Harvey P. Dale, Dec 23 2011 *)

c=0; o=2; s=1; forprime(p=3,default(primelimit), p>s & s*=10; isprime(o*s+o=p) & write("b030460.txt",c++," ",p))  \\ M. F. Hasler, Feb 06 2011

A030459(n) = A151799(a(n)). - M. F. Hasler, Feb 06 2011

A030461(n) = concat(A030459(n),a(n)) = A045533( A000720( A030459(n))). - M. F. Hasler, Feb 06 2011

Offset changed from 0 to 1 by M. F. Hasler, Feb 06 2011

A034591 Numbers whose concatenation with the next prime yields a prime.

Original entry on oeis.org

0, 2, 6, 8, 9, 12, 27, 31, 36, 42, 44, 45, 51, 56, 63, 68, 69, 78, 83, 86, 93, 94, 96, 98, 102, 104, 105, 108, 115, 117, 118, 123, 126, 132, 138, 150, 151, 154, 156, 157, 160, 167, 176, 180, 183, 186, 192, 194, 195, 199, 201, 205, 213, 217, 219, 225, 230, 233

Offset: 1

Patrick De Geest, Oct 15 1998

			8 is a term because nextprime(8) = 11 and 811 is prime.

See also A034592, A034593, A034594, A034596, A030459.

Select[Range[0,250],PrimeQ@FromDigits@Flatten[IntegerDigits/@{#,NextPrime@#}]&] (* Giorgos Kalogeropoulos, Jul 30 2021 *)

isok(m) = isprime(eval(Str(m, nextprime(m+1)))); \\ Michel Marcus, Oct 03 2014 and Jul 30 2021

A034593 Cycle of 3 steps possible for 'concatenate a(n) and nextprime(a(n)) is a prime'.

Original entry on oeis.org

467, 941, 8834, 9548, 13012, 22302, 23592, 26208, 47538, 58578, 78910, 86447, 86925, 116230, 118040, 123716, 128055, 213493, 234146, 238326, 273057, 285315, 286422, 389336, 399261, 457810, 468764, 481476, 502590, 525402, 541102, 570205

Offset: 0

Patrick De Geest, Oct 15 1998

			a(n)=78910 -> nextprime(a(n)) is 78919 so '7891078919' is prime (=step 1); a(n2)=7891078919 -> nextprime(a(n2)) is 7891078931 so '78910789197891078931' is prime (=step 2); a(n3)=78910789197891078931 -> nextprime(a(n3)) is 78910789197891078949 so '7891078919789107893178910789197891078949' is prime (=step 3).

A036341 Concatenation of prime p and nextprime(p) is prime -> cycles of 4 steps possible.

Original entry on oeis.org

127787377, 1510818931, 3147482977, 3307903909, 3621408103, 3964636549, 7224979183, 7881628361, 8043354509, 8740618759, 10091655397, 10164789521, 10194261067, 10380609119, 10436432219, 11472028801, 12059694769, 13887362681, 14880879703, 15197340049

Offset: 1

Patrick De Geest, Dec 15 1998

a(1)-a(5) found by Jo Yeong Uk (hyukjo(AT)sigma.chungnam.ac.kr).

Giovanni Resta, Table of n, a(n) for n = 1..4000
Carlos Rivera, Puzzle 29. P_i = P_(i-1) & nxtprm(P_(i-1)), P_i = prime for i => 1, The Prime Puzzles and Problems Connection.

Cf. A030459, A034593, A036339, A036340.

Offset corrected and terms a(6) and beyond added by Giovanni Resta, May 14 2020

A034594 Concatenation of nextprime(a(n)) and a(n) is a prime.

Original entry on oeis.org

3, 27, 33, 39, 47, 51, 53, 61, 63, 91, 111, 123, 129, 131, 143, 173, 189, 199, 211, 217, 219, 231, 233, 237, 257, 273, 279, 301, 319, 341, 353, 357, 417, 423, 429, 473, 481, 489, 493, 501, 519, 523, 529, 531, 537, 551, 561, 573, 579, 587, 597, 607, 609, 619

Offset: 1

Patrick De Geest, Oct 15 1998

			a(n)=27 -> nextprime(a(n)) is 29 so '2927' is a prime.

Andrew Howroyd, Table of n, a(n) for n = 1..10000

A036339 Concatenation of prime p and nextprime(p) is prime -> cycles of 2 steps possible.

Original entry on oeis.org

467, 941, 13681, 14461, 21787, 22171, 22369, 24049, 24151, 25457, 29333, 37397, 41221, 42467, 43481, 46511, 48023, 54133, 56681, 68699, 75883, 85081, 101341, 103511, 117443, 120193, 126199, 137363, 144323, 145133, 158791, 175853, 181891, 183797

Offset: 1

Patrick De Geest, Dec 15 1998

C. Rivera, Details of procedure

Cf. A030459, A034592, A036340, A036341.

Offset corrected and missing 181891 inserted by Sean A. Irvine, Oct 26 2020

cp's OEIS Frontend

A001359 Lesser of twin primes.

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A030461 Primes that are concatenations of two consecutive primes.

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A086040 Prime p concatenated with next 4 primes is also prime.

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A174031 The smallest integer k>0 such that the double-concatenation prime(n) // prime(n+1) // k is a prime number.

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A030460 Previous prime concatenated with this prime p is a prime.

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A034591 Numbers whose concatenation with the next prime yields a prime.

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A034593 Cycle of 3 steps possible for 'concatenate a(n) and nextprime(a(n)) is a prime'.

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