A180950 -id:A180950 - cp's OEIS frontend

A073681 Smallest of three consecutive primes whose sum is a prime.

5, 7, 11, 17, 19, 23, 29, 31, 41, 53, 61, 67, 71, 79, 83, 101, 109, 139, 149, 157, 163, 197, 211, 229, 271, 281, 283, 293, 311, 337, 347, 349, 379, 389, 401, 409, 431, 449, 457, 463, 467, 491, 499, 509, 547, 617, 641, 653, 659, 661, 701, 719, 743, 751, 757

Offset: 1

Amarnath Murthy, Aug 11 2002

nonn

Hugo Pfoertner, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Harry J. Smith)

Cf. A152469, A152470, A174742, A034962, A152468, A180948, A189571, A180950, A226380.

[NthPrime(n): n in [0..200] | IsPrime(NthPrime(n)+NthPrime(n+1)+ NthPrime(n+2))]; // Vincenzo Librandi, May 06 2015

t0:=[];
t1:=[];
t2:=[];
for i from 1 to 1000 do
t3:=ithprime(i)+ithprime(i+1)+ithprime(i+2);
if isprime(t3) then
t0:=[op(t0),i];
t1:=[op(t1),ithprime(i)];
t2:=[op(t2),ithprime(i+2)];
fi;
od:
t1;

Transpose[Select[Partition[Prime[Range[200]],3,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jan 25 2012 *)

forprime(p=1,1000, pp=nextprime(p+1); if(isprime(p+pp+nextprime(pp+1)),print1(p",")))

A073681(n,print_all=0,start=3)={my(r,q=1);forprime(p=start,, isprime(r+(r=q)+(q=p)) & (n-- ||return(precprime(r-1))) & print_all & print1(precprime(r-1)","))} \\ M. F. Hasler, Dec 18 2012

Conjecture: for n -> oo, a(n) ~ prime(n) * (log(prime(n)))^C, where C = 8/Pi^2 (cf. A217739). - Alain Rocchelli, Sep 04 2023

More terms from Ralf Stephan, Mar 20 2003

More cross-references from Harvey P. Dale, Jun 05 2013

A152468 Smallest of five consecutive primes whose sum is a prime.

Original entry on oeis.org

5, 7, 11, 13, 19, 29, 31, 43, 53, 59, 67, 73, 79, 107, 109, 113, 127, 137, 149, 151, 157, 163, 179, 191, 211, 223, 229, 263, 269, 307, 311, 349, 353, 359, 379, 383, 401, 409, 419, 433, 443, 449, 461, 467, 479, 521, 523, 541, 557, 569, 571, 577, 599, 613, 619

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

nonn

Surprisingly many terms are also in A073681. - Zak Seidov, Dec 17 2012

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A073681, A034965, A180948, A189571, A180950, A226380.

lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];p3=Prime[n+3];p4=Prime[n+4];If[PrimeQ[p=p0+p1+p2+p3+p4],AppendTo[lst,p0]],{n,6!}];lst
Transpose[Select[Partition[Prime[Range[500]], 5, 1], PrimeQ[Total[#]] &]][[1]] (* Harvey P. Dale, Jun 05 2013 *)
Prime[Select[Range[150], PrimeQ[Sum[Prime[# + i], {i, 0, 4}]] &]] (* Bruno Berselli, Aug 21 2013 *)

{a=2; b=3; c=5; d=7; e=11; for(n=1,100, s=a+b+c+d+e;
if(isprime(s), print1(a", ")); a=b; b=c; c=d; d=e; e=nextprime(e+2))} /* Zak Seidov, Dec 17 2012 */

More cross references from Harvey P. Dale, Jun 05 2013

A180948 Smallest of seven (7) consecutive primes whose sum is a prime.

Original entry on oeis.org

17, 19, 23, 29, 31, 43, 47, 53, 61, 71, 79, 89, 97, 103, 107, 113, 127, 137, 151, 233, 257, 313, 317, 359, 367, 373, 379, 383, 401, 461, 463, 487, 499, 503, 509, 521, 577, 587, 617, 619, 761, 797, 821, 827, 839, 853, 881, 883, 907, 1019, 1061, 1063, 1069, 1097

Offset: 1

Carmine Suriano, Sep 27 2010

nonn

There are twins such as (17,19); (461,463); (1061,1063).

There are also consecutives such as (17,19,23,29,31); (359,367,373,379,383); (1949,1951,1973).

			a(7)=47+53+59+61+67+71+73=431 is a prime.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A000040, A073681, A082246, A152468, A189571, A180950, A226380.

Transpose[Select[Partition[Prime[Range[500]],7,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)

More cross references from Harvey P. Dale, Jun 05 2013

A226380 Smallest of 101 consecutive primes whose sum is prime.

Original entry on oeis.org

83, 89, 139, 179, 181, 277, 281, 353, 409, 479, 499, 521, 571, 587, 643, 727, 839, 883, 887, 919, 929, 971, 977, 1019, 1021, 1117, 1213, 1223, 1237, 1259, 1303, 1327, 1367, 1381, 1399, 1423, 1433, 1481, 1483, 1667, 1723, 1789, 1823, 1861, 1879, 1913, 2083

Offset: 1

Harvey P. Dale, Jun 05 2013

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

Cf. A073681, A152468, A180948, A189571, A180950.

Transpose[Select[Partition[Prime[Range[500]],101,1],PrimeQ[Total[#]]&]] [[1]]
Prime[Select[Range[400], PrimeQ[Sum[Prime[# + i], {i, 0, 100}]] &]] (* Bruno Berselli, Aug 21 2013 *)

A189571 Smallest of nine consecutive primes whose sum is a prime.

Original entry on oeis.org

3, 29, 31, 37, 47, 79, 83, 89, 107, 109, 127, 131, 139, 149, 157, 173, 179, 193, 197, 199, 211, 241, 277, 347, 359, 367, 373, 389, 397, 433, 449, 487, 491, 521, 577, 593, 619, 643, 659, 677, 743, 761, 829, 853, 953, 977, 1049, 1063, 1087, 1129, 1151, 1193

Offset: 1

Bruno Berselli, Apr 23 2011

nonn

First 7-tuple of consecutive primes belonging to the sequence: 118061, 118081, 118093, 118127, 118147, 118163, 118169. Twin primes in the sequence: 29, 31; 107, 109; 197, 199; 1427, 1429; 1607, 1609; 1721, 1723; 4019, 4021, etc. [Bruno Berselli, Aug 26 2013]

			47 is in the sequence because 47+53+59+61+67+71+73+79+83 = 593 and 593 is prime.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A073681, A152468, A180948, A180950, A226380.

[ NthPrime(n): n in [1..190] | IsPrime(&+[NthPrime(n+s): s in [0..8]]) ];

Transpose[Select[Partition[Prime[Range[500]],9,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)

from sympy import isprime, nextprime
def aupto(limit):
  plst, alst = [3, 5, 7, 11, 13, 17, 19, 23, 29], []
  while plst[0] <= limit:
    if isprime(sum(plst)): alst.append(plst[0])
    plst = plst[1:] + [nextprime(plst[-1])]
  return alst
print(aupto(1200)) # Michael S. Branicky, Mar 29 2021

Additional cross reference from Harvey P. Dale, Jun 05 2013

A089793 a(n) = the first prime in the earliest chain of 2n+1 consecutive primes whose sum is prime.

Original entry on oeis.org

2, 5, 5, 17, 3, 5, 29, 3, 3, 11, 7, 7, 5, 7, 13, 13, 7, 5, 5, 13, 7, 7, 7, 7, 11, 17, 3, 3, 97, 29, 3, 13, 3, 19, 19, 3, 5, 3, 23, 7, 11, 53, 31, 89, 53, 19, 11, 3, 17, 23, 83, 11, 5, 47, 37, 5, 17, 3, 3, 29, 23, 5, 5, 5, 59, 7, 7, 31, 3, 67, 3, 3, 89, 71, 31

Offset: 0

Joseph L. Pe, Jan 09 2004

nonn

In general (except possibly when it begins with 2), the sum of an even number of consecutive primes is even - hence the restriction to odd chain lengths.

			17 is the first prime in the chain 17, 19, 23, 29, 31, 37, 41, which is the earliest chain of 2 * 3 + 1 = 7 consecutive primes whose sum, 197, is prime. Hence a(3) = 17.

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. A070934, A215235, A180950, A226380.

With[{prs=Prime[Range[1000]]},First[#]&/@Flatten[Table[Select[ Partition[ prs,2n+1,1],PrimeQ[Total[#]]&,1],{n,0,80}],1]] (* Harvey P. Dale, Jun 21 2013 *)

A228201 Smallest of 11 consecutive primes whose sum is not a prime.

Original entry on oeis.org

2, 3, 17, 29, 31, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 127, 131, 139, 163, 179, 181, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 271, 277, 311, 313, 317, 337, 347, 367, 373, 379, 383, 389, 397, 401, 409, 419, 433, 439, 443, 449

Offset: 1

Vincenzo Librandi, Aug 20 2013

nonn

			31 is in the sequence because 31+37+41+43+47+53+59+61+67+71+73 = 583 and 583 = 11*53.

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

Cf. A180950, A000040.

[NthPrime(n): n in [1..120] |not IsPrime(&+[NthPrime(n+s): s in [0..10]])];

Transpose[Select[Partition[Prime[Range[150]], 11, 1], ! PrimeQ[Total[#]] &]][[1]]
Prime[Select[Range[100], ! PrimeQ[Sum[Prime[# + i], {i, 0, 10}]] &]] (* Bruno Berselli, Aug 22 2013 *)

A229059 Smallest of 13 consecutive primes whose sum is a prime.

Original entry on oeis.org

29, 41, 47, 61, 71, 89, 97, 103, 107, 131, 139, 149, 193, 211, 241, 263, 277, 293, 311, 313, 349, 353, 379, 383, 397, 401, 419, 443, 461, 491, 521, 557, 593, 599, 631, 647, 677, 739, 761, 809, 827, 877, 983, 1013, 1039, 1061, 1109, 1117, 1171, 1193, 1201

Offset: 1

Vincenzo Librandi, Sep 13 2013

nonn

			a(1)=29 since 29+31+37+41+43+47+53+59+61+67+71+73+79=691 is a prime.

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

Cf. A073681, A152468, A180948, A189571, A180950, A226380.

[NthPrime(n): n in [1..200] | IsPrime(&+[NthPrime(n+s): s in [0..12]])];

Transpose[Select[Partition[Prime[Range[250]], 13, 1], PrimeQ[Total[#]]&]][[1]]

cp's OEIS Frontend

A073681 Smallest of three consecutive primes whose sum is a prime.

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A152468 Smallest of five consecutive primes whose sum is a prime.

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A180948 Smallest of seven (7) consecutive primes whose sum is a prime.

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A226380 Smallest of 101 consecutive primes whose sum is prime.

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A189571 Smallest of nine consecutive primes whose sum is a prime.

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A089793 a(n) = the first prime in the earliest chain of 2n+1 consecutive primes whose sum is prime.

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Mathematica

A228201 Smallest of 11 consecutive primes whose sum is not a prime.

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Magma

Mathematica

A229059 Smallest of 13 consecutive primes whose sum is a prime.

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