A180948 -id:A180948 - 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

A082246 Primes that are the sum of 7 consecutive primes.

Original entry on oeis.org

197, 223, 251, 281, 311, 401, 431, 463, 523, 593, 659, 719, 757, 827, 863, 947, 991, 1063, 1171, 1753, 1901, 2347, 2393, 2647, 2689, 2731, 2777, 2819, 2953, 3347, 3389, 3533, 3643, 3701, 3761, 3821, 4177, 4217, 4451, 4493, 5507, 5717, 5849, 5927, 6029

Offset: 1

Cino Hilliard, May 09 2003

			2 + 3 + 5 + 7 + 11 + 13 + 17 = 58 = 2*29
3 + 5 + 7 + 11 + 13 + 17 + 19 = 75 = 3*5^2
5 + 7 + 11 + 13 + 17 + 19 + 23 = 95 = 5*19
7 + 11 + 13 + 17 + 19 + 23 + 29 = 119 = 7*17
11 + 13 + 17 + 19 + 23 + 29 + 31 = 143 = 11*13
13 + 17 + 19 + 23 + 29 + 31 + 37 = 169 = 13*13
17 + 19 + 23 + 29 + 31 + 37 + 41 = 197 (prime)

Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Cf. A180948.

Primes:= select(isprime, [seq(i,i=3..10000,2)]):
S:= ListTools:-PartialSums(Primes):
select(isprime,S[8..-1]-S[1..-8]); # Robert Israel, Dec 14 2017

Select[ListConvolve[{1,1,1,1,1,1,1},Prime[Range[200]]],PrimeQ] (* Harvey P. Dale, Jul 12 2013 *)
Select[Total/@Partition[Prime[Range[200]],7,1],PrimeQ] (* Harvey P. Dale, Jul 24 2017 *)

\\ primes in the sum of m odd number of consecutive primes. m=7
psumprm(m,n) = { sr=0; s=0; for(j=1,m, s+=prime(j); ); for(x=1,n, s = s - prime(x)+ prime(x+m); if(isprime(s),sr+=1.0/s; print1(s" ")); ); print(); print(sr) }

Corrected by Michael Somos, Feb 01 2004

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

A180950 Smallest prime such that the sum of successive 11 primes is a prime.

Original entry on oeis.org

5, 7, 11, 13, 19, 23, 37, 41, 59, 101, 103, 107, 109, 113, 137, 149, 151, 157, 167, 173, 191, 269, 281, 283, 293, 307, 331, 349, 353, 359, 421, 431, 463, 479, 487, 499, 503, 569, 599, 607, 613, 617, 619, 677, 733, 761, 773, 823, 853, 883, 967, 977, 1051, 1087

Offset: 1

Carmine Suriano, Sep 27 2010

nonn

Sum i=0 to 10 of prime(n+i) is a prime.
There are many twins: (11,13); (149,151); (1301,1303); (1997,1999); (8969,8971) ...
There are also consecutive primes: (101,103,107,109,113); (607,613,617,619); (8681,8689,8693)

			a(5)=19 since 19+23+29+31+37+41+43+47+53+59+61=443 is a prime.

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

Cf. A000040, A127338, A073681, A152468, A180948, A189571, A226380.

Transpose[Select[Partition[Prime[Range[500]], 11, 1], PrimeQ[Total[#]] &]][[1]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)
Prime[Select[Range[200], PrimeQ[Sum[Prime[# + i], {i, 0, 10}]] &]] (* Bruno Berselli, Aug 22 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

A370139 Primes p such that the sums of three, five, and seven consecutive primes starting with p are prime.

Original entry on oeis.org

19, 29, 31, 53, 79, 379, 401, 839, 883, 1301, 1409, 1951, 1973, 2113, 2683, 2791, 2833, 3407, 3613, 3793, 3823, 4441, 4751, 4831, 5623, 5827, 6133, 6329, 7187, 7237, 7703, 8527, 9173, 10103, 10853, 11317, 12277, 13163, 13933, 14159, 14827, 15241, 15667

Offset: 1

Harvey P. Dale, Feb 11 2024

nonn

			379 is in the sequence because the seven consecutive primes starting with 379 are 379, 383, 389, 397, 401, 409, and 419, and (379+383+389)=1151, and (379+383+389+397+401)=1949, and (379+383+389+397+401+409+419)=2777, and 1151 and 1949 and 2777 are all primes.

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

Intersection of A180948 and A182121.

Select[Partition[Prime[Range[5000]],7,1],AllTrue[{Total[Take[#,3]],Total[Take[#,5]],Total[#]},PrimeQ]&][[;;,1]]

A228199 Smallest of 7 consecutive primes whose sum is not a prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 37, 41, 59, 67, 73, 83, 101, 109, 131, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 263, 269, 271, 277, 281, 283, 293, 307, 311, 331, 337, 347, 349, 353, 389, 397, 409, 419, 421, 431, 433, 439, 443

Offset: 1

Vincenzo Librandi, Aug 20 2013

nonn

			59 is in the sequence because 59+61+67+71+73+79+83 = 493 and 493 is not a prime.

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

Cf. A000040, A180948.

[NthPrime(n): n in [1..120] |not IsPrime(&+[NthPrime(n+s): s in [0..6]])];

Transpose[Select[Partition[Prime[Range[150]], 7, 1], ! PrimeQ[Total[#]] &]][[1]]
Prime[Select[Range[100], ! PrimeQ[Sum[Prime[# + i], {i, 0, 6}]] &]] (* 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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A082246 Primes that are the sum of 7 consecutive primes.

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

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A180950 Smallest prime such that the sum of successive 11 primes 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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A370139 Primes p such that the sums of three, five, and seven consecutive primes starting with p are prime.

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Mathematica

A228199 Smallest of 7 consecutive primes whose sum is not a prime.