1,1

Integers in this sequence can never be prime, as, starting from the second one, they are all multiples of 3.

Robert Israel,Table of n, a(n) for n = 1..9832

List: concatenate(p, p+100) iff p and p+100 are primes.

9191019 is in this sequence because 919 is prime, 919+100 = 1019 is prime and 9191019 is the concatenation of those two primes differing by 100.

f:= proc(n) if isprime(n) and isprime(n+100) then 10^(1+ilog10(n+100))*n+n+100 fi end proc:

map(f, [3, seq(i, i=7..1000, 6)]); #Robert Israel,Dec 07 2015

FromDigits[Join@@IntegerDigits/@{#, #+100}]&/@Select[Prime@Range@200, PrimeQ[#+100]&] (*Giorgos Kalogeropoulos,Jul 04 2021 *)

(Python)

from sympy import isprime, primerange as prange

def auptop(lim):

return [int(str(p)+str(p+100)) for p in prange(2, lim+1) if isprime(p+100)]

print(auptop(577)) #Michael S. Branicky,Jul 04 2021

Cf.A000040,A001358,A023201,A100750,A103195,A103206,A104718,A104719.

base,easy,nonn

Jonathan Vos Post,Mar 21 2005

approved

1,1

All terms are multiples of 3.

a(n) = Concatenate(P, P+1000) iff P prime and P+1000 prime.

1811181 is in this sequence because 181 is prime, 181+1000 = 1181 is prime and those two primes are concatenated.

10001#+1000&/@Select[Prime[Range[150]], PrimeQ[#+1000]&] (*Harvey P. Dale,Sep 01 2017 *)

Cf.A100750,A103195,A103206,A104718,A104719,A103523.

base,easy,nonn

Jonathan Vos Post,Mar 22 2005

approved

1,1

After the first element, 31000003, which is prime, integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for 3671000367 = 3 x 1223666789, 4571000457 = 3 x 1523666819, 5411000541 = 3 x 1803666847, 9071000907 = 3 x 3023666969.

a(n) = Concatenate(P, P+1000000) iff P prime and P+1000000 prime.

Prime(47) = 211 and 211 + 1000000 = Prime(78515) = 1000211. Concatenating these two primes gives 2111000211 = 3^4 * 17^2 * 31 * 2909.

Cf.A000040,A001358,A023201,A100750,A103195,A103206,A104718,A104719,A103523,A103534.

base,easy,nonn

Jonathan Vos Post,Mar 23 2005

approved

1,1

Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(42) concatenated with Prime(50847544) = 1811000000181 = 3 x 603666666727.

Harvey P. Dale,Table of n, a(n) for n = 1..1000

a(n) = Concatenate(P, P+1000000000) iff P prime and P+1000000000 prime.

181 is prime, 181+10^9 = 1000000181 is prime, so their concatenation is an element of this sequence: 1811000000181. Coincidentally, prime(181)+10^9 = 1000001087 is also prime.

FromDigits[Join[IntegerDigits[#], IntegerDigits[#+10^9]]]&/@Select[Prime[ Range[ 200]], PrimeQ[ #+ 10^9]&] (*Harvey P. Dale,May 14 2022 *)

Cf.A000040,A001358,A023201,A100750,A103195,A103206,A104718,A104719,A103523,A103534,A103576.

base,easy,nonn

Jonathan Vos Post,Mar 25 2005

approved

1,1

Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(177) concatenated with Prime(37607912056) = 10511000000001051 = 3 * 3503666666667017.

Harvey P. Dale,Table of n, a(n) for n = 1..1000

a(n) = Concatenate(P, P+10^12) iff P prime and P+10^12 prime.

61 is prime, specifically prime(18) and 61 + 10^12 is prime, specifically prime(7607912020), so their concatenation is in this sequence: 611000000000061. The concatenation is not itself prime, as it equals 3 * 7 * 23 * 1265010351967.

#*10^13+10^12+#&/@Select[Prime[Range[200]], PrimeQ[#+10^12]&] (*Harvey P. Dale,Jan 18 2021 *)

Cf.A000040,A001358,A023201,A100750,A103195,A103206,A104718,A104719,A103523,A103534,A103576,A103617.

base,easy,nonn

Jonathan Vos Post,Mar 29 2005

approved

1,1

Subsequence ofA100750.

Vincenzo Librandi,Table of n, a(n) for n = 1..1000

a(1) = 3+100=103, a(2)=7+100=107, a(3)=13+100=113.

Select[Prime[Range[200]] + 100, PrimeQ] (*Vincenzo Librandi,Sep 12 2013 *)

(Magma) [p+100: p in PrimesUpTo(1200)| IsPrime(p+100)]; //Vincenzo Librandi,Sep 12 2013

nonn,easy

Vincenzo Librandi,Sep 14 2009

Definition rephrased, relation toA100750added, 563, 719 etc. inserted -R. J. Mathar,Sep 16 2009

approved