A152468 -id:A152468 - 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

A034965 Primes that are sum of five consecutive primes.

Original entry on oeis.org

53, 67, 83, 101, 139, 181, 199, 263, 311, 331, 373, 421, 449, 587, 617, 647, 683, 733, 787, 811, 839, 863, 941, 991, 1123, 1151, 1193, 1361, 1381, 1579, 1609, 1801, 1831, 1861, 1949, 1979, 2081, 2113, 2143, 2221, 2273, 2297, 2357, 2423, 2459, 2689, 2731

Offset: 1

Patrick De Geest, Oct 15 1998

nonn

			53 = 5 + 7 + 11 + 13 + 17.
373 = 67 + 71 + 73 + 79 + 83.

Harvey P. Dale and Syed Iddi Hasan, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A001043, A011974, A034707, A152468. Also Cf. A034964, of which this sequence is a subset.

ts_prod_n:=proc(n) local i,ans; ans:=[ ]: for i from 1 to n do if isprime(ithprime(i)+ithprime(i+1)+ithprime(i+2)+ithprime(i+3)+ithprime(i+4))= 'true' then ans:=[op(ans), ithprime(i)+ithprime(i+1)+ithprime(i+2)+ithprime(i+3)+ithprime(i+4) ]: fi od: end: ts_prod_n(701); # Jani Melik, May 05 2006

Select[Table[Plus@@Prime[Range[n, n + 4]], {n, 200}], PrimeQ] (* Alonso del Arte, Dec 30 2011 *)
Select[Total/@Partition[Prime[Range[200]],5,1],PrimeQ] (* Harvey P. Dale, May 24 2012 *)

Corrected example by Paul S. Coombes, Dec 29 2011

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

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

A152470 Largest of three consecutive primes whose sum is a prime.

Original entry on oeis.org

11, 13, 17, 23, 29, 31, 37, 41, 47, 61, 71, 73, 79, 89, 97, 107, 127, 151, 157, 167, 173, 211, 227, 239, 281, 293, 307, 311, 317, 349, 353, 359, 389, 401, 419, 421, 439, 461, 463, 479, 487, 503, 509, 523, 563, 631, 647, 661, 673, 677, 719, 733, 757, 761, 769

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

nonn

			3+5+7 = 15 is composite.
5+7+11 = 23 is prime and (5, 7, 11) are consecutive primes so a(1) = 11.

Pierre CAMI, Table of n, a(n) for n = 1..10000

Cf. A073681, A072225, A152468, A152469.

Primes:= select(isprime,[2,(2*i+1 $ i=1..10000)]):
Primes[select(t -> isprime(Primes[t-2]+Primes[t-1]+Primes[t]),[$3..nops(Primes)])];
# Robert Israel, Aug 29 2014

lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];If[PrimeQ[p0+p1+p2],AppendTo[lst,p2]],{n,6!}];lst

s=[]; for(n=1, 1000, if(isprime(prime(n)+prime(n+1)+prime(n+2)), s=concat(s, prime(n+2)))); s \\ Colin Barker, Aug 25 2014

A152469 Second smallest of three consecutive primes whose sum is a prime.

Original entry on oeis.org

7, 11, 13, 19, 23, 29, 31, 37, 43, 59, 67, 71, 73, 83, 89, 103, 113, 149, 151, 163, 167, 199, 223, 233, 277, 283, 293, 307, 313, 347, 349, 353, 383, 397, 409, 419, 433, 457, 461, 467, 479, 499, 503, 521, 557, 619, 643, 659, 661, 673, 709, 727, 751, 757, 761

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

nonn

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

Cf. A073681, A072225, A152468, A152470.

t0:=[];
t1:=[];
t2:=[];
t3:=[];
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+1)];
t3:=[op(t2),ithprime(i+2)];
fi;
od:
t2;

lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];If[PrimeQ[p0+p1+p2],AppendTo[lst,p1]],{n,6!}];lst
Select[Partition[Prime[Range[200]],3,1],PrimeQ[Total[#]]&][[All,2]] (* Harvey P. Dale, May 08 2021 *)

A182121 Primes p such that the sum of both three and five consecutive primes starting with p is prime.

Original entry on oeis.org

5, 7, 11, 19, 29, 31, 53, 67, 79, 109, 149, 157, 163, 211, 229, 311, 349, 379, 401, 409, 449, 467, 653, 757, 809, 839, 857, 863, 883, 983, 997, 1033, 1087, 1103, 1187, 1193, 1289, 1301, 1303, 1409, 1481, 1523, 1553, 1637, 1663, 1669, 1709, 1951, 1973

Offset: 1

Zak Seidov, Dec 17 2012

nonn

			5 is in the sequence because 5 + 7 + 11 = 23 is prime and 5 + 7 + 11 + 13 + 17 = 53 is also prime.

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

Intersection of A073681 and A152468.

cpQ[n_]:=Module[{ppi=PrimePi[n],cnsc},cnsc=Prime[Range[ppi,ppi+4]];And@@ PrimeQ[ {Total[cnsc],Total[Take[cnsc,3]]}]]; Select[Prime[Range[300]],cpQ] (* Harvey P. Dale, Mar 28 2013 *)
Select[Partition[Prime[Range[500]],5,1],AllTrue[{Total[Take[#,3]],Total[#]},PrimeQ]&][[;;,1]] (* Harvey P. Dale, Feb 11 2024 *)

{a=2;b=3;c=5;d=7;e=11;for(n=1,300,s=a+b+c+d+e;
if(isprime(s)&&isprime(a+b+c),print1(a","));a=b;b=c;c=d;d=e;e=nextprime(e+2))}

A211170 Primes that are sum of both three and five consecutive primes.

Original entry on oeis.org

83, 199, 311, 941, 1151, 1381, 2357, 3121, 4337, 4363, 4957, 5059, 7039, 8069, 8117, 8161, 8389, 8627, 8819, 8971, 9011, 9349, 10211, 10253, 13127, 14813, 16249, 19207, 19717, 21377, 23143, 24329, 32983, 34807, 38113, 39623, 41141, 44279, 45061, 45979, 58403

Offset: 1

Zak Seidov, Jan 31 2013

nonn

Intersection of A034962 and A034965.

			a(1) = 83 = A034962(6) = 23 + 29 + 31 = A034965(3) = 11 + 13 + 17 + 19 + 23.

Donovan Johnson, Table of n, a(n) for n = 1..10000

Cf. A034962, A034965, A073681, A152468.

Module[{prs=Prime[Range[3000]],pr3,pr5},pr3=Select[Total/@Partition[ prs, 3, 1], PrimeQ];pr5=Select[Total/@Partition[prs,5,1],PrimeQ];Intersection[ pr3,pr5]] (* Harvey P. Dale, Oct 24 2016 *)

cp's OEIS Frontend

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

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A034965 Primes that are sum of five consecutive primes.

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A180948 Smallest of seven (7) 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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A152470 Largest of three consecutive primes whose sum is a prime.

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