A103206 -id:A103206 - cp's OEIS frontend

A104719 Concatenations of pairs of primes that differ by 10.

313, 717, 1323, 1929, 3141, 3747, 4353, 6171, 7383, 7989, 97107, 103113, 127137, 139149, 157167, 163173, 181191, 223233, 229239, 241251, 271281, 283293, 307317, 337347, 349359, 373383, 379389, 409419, 421431, 433443, 439449, 457467, 499509

Offset: 1

Jonathan Vos Post and Parthasarathy Nambi, Mar 20 2005

There are no primes in this sequence after a(1) = 313, as all values thereafter are divisible by 3. Semiprimes in this sequence include: a(2) = 717 = 3 * 239, a(4) = 1929 = 3 * 643, a(6) = 3747 = 3 * 1249, a(7) = 4353 = 3 * 1451, a(10) = 7989 = 3 * 2663, a(11) = 97107 = 3 * 32369, a(13) = 127137 = 3 * 42379, a(17) = 181191 = 3 * 60397, a(18) = 223233 = 3 * 74411, a(29) = 421431 = 3 * 140477, a(30) = 433443 = 3 * 144481, a(34) = 547557 = 3 * 182519, a(35) = 577587 = 3 * 192529, a(40) = 691701 = 3 * 230567, a(41) = 709719 = 3 * 236573, a(49) = 919929 = 3 * 306643, a(52) = 10091019 = 3 * 3363673.

			Primes 3 and 13 differ by 10.

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

Cf. A000040, A001358, A023202, A103195, A103206, A104718.

FromDigits[Join[IntegerDigits[#],IntegerDigits[#+10]]]&/@Select[ Prime[ Range[ 100]], PrimeQ[ #+10]&] (* Harvey P. Dale, Jun 14 2015 *)

a(n) = A023203(n) concatenated with A023203(n)+10.

A104718 Concatenations of pairs of primes that differ by 8.

Original entry on oeis.org

311, 513, 1119, 2331, 2937, 5361, 5967, 7179, 8997, 101109, 131139, 149157, 173181, 191199, 233241, 263271, 269277, 359367, 389397, 401409, 431439, 449457, 479487, 491499, 563571, 569577, 593601, 599607, 653661, 683691, 701709, 719727, 743751

Offset: 1

Jonathan Vos Post, Mar 20 2005

There are no primes in this sequence after a(1) = 311, as all values thereafter are divisible by 3. Semiprimes in this sequence include: a(3) = 1119 = 3 * 373 a(6) = 5361 = 3 * 1787, a(8) = 7179 = 3 * 2393, a(9) = 8997 = 3 * 2999, a(10) = 101109 = 3 * 33703, a(13) = 173181 = 3 * 57727, a(15) = 233241 = 3 * 77747, a(17) = 269277 = 3 * 89759, a(21) = 431439 = 3 * 143813, a(26) = 569577 = 3 * 189859, a(35) = 821829 = 3 * 273943.

Cf. A000040, A001358, A023202, A103195, A103206, A104719.

a(n) = A023202(n) concatenated with A023202(n)+8.

A103523 Concatenations of pairs of primes that differ by 100.

Original entry on oeis.org

3103, 7107, 13113, 31131, 37137, 67167, 73173, 79179, 97197, 127227, 139239, 151251, 157257, 163263, 181281, 193293, 211311, 283383, 331431, 349449, 367467, 379479, 409509, 421521, 457557, 463563, 487587, 499599, 541641, 547647, 577677

Offset: 1

Jonathan Vos Post, Mar 21 2005

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

			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.

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

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

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 *)

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

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

A103534 Concatenations of pairs of primes that differ by 1000.

Original entry on oeis.org

131013, 191019, 311031, 611061, 971097, 1031103, 1091109, 1511151, 1631163, 1811181, 1931193, 2231223, 2291229, 2771277, 2831283, 3071307, 3671367, 3731373, 4091409, 4331433, 4391439, 4871487, 4991499, 5231523, 5711571

Offset: 1

Jonathan Vos Post, Mar 22 2005

All terms are multiples of 3.

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

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

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

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

A103576 Concatenations of pairs of primes that differ by 1000000.

Original entry on oeis.org

31000003, 371000037, 1511000151, 1931000193, 1991000199, 2111000211, 3131000313, 3671000367, 3971000397, 4091000409, 4571000457, 5411000541, 5471000547, 5771000577, 6191000619, 6911000691, 8291000829, 8591000859

Offset: 1

Jonathan Vos Post, Mar 23 2005

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.

			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.

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

A103617 Concatenations of pairs of primes that differ by 10^9.

Original entry on oeis.org

71000000007, 971000000097, 1031000000103, 1811000000181, 2231000000223, 2411000000241, 2711000000271, 3491000000349, 4091000000409, 4331000000433, 4391000000439, 6071000000607, 6131000000613, 7871000000787, 8291000000829

Offset: 1

Jonathan Vos Post, Mar 25 2005

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.

			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.

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

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

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

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

A104873 Concatenations of pairs of primes that differ by 10^12.

Original entry on oeis.org

611000000000061, 1631000000000163, 1931000000000193, 2111000000000211, 2711000000000271, 3311000000000331, 5471000000000547, 6611000000000661, 7511000000000751, 7871000000000787, 9971000000000997, 10511000000001051

Offset: 1

Jonathan Vos Post, Mar 29 2005

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.

			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.

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

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

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

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

cp's OEIS Frontend

A104719 Concatenations of pairs of primes that differ by 10.

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A104718 Concatenations of pairs of primes that differ by 8.

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A103523 Concatenations of pairs of primes that differ by 100.

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A103534 Concatenations of pairs of primes that differ by 1000.

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A103576 Concatenations of pairs of primes that differ by 1000000.

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A103617 Concatenations of pairs of primes that differ by 10^9.

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A104873 Concatenations of pairs of primes that differ by 10^12.

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