A053184 -id:A053184 - cp's OEIS frontend

A290767 Primes p such that p^2 +/- p +/- 1 are all nonprimes.

23, 37, 43, 73, 107, 109, 113, 137, 157, 179, 211, 223, 227, 229, 239, 251, 257, 271, 277, 283, 311, 313, 317, 347, 353, 367, 389, 439, 443, 467, 503, 509, 521, 523, 547, 557, 563, 577, 587, 593, 601, 631, 653, 661, 719, 733, 757, 797, 811, 821, 823, 829, 853, 859, 877, 883

Offset: 1

Ralf Steiner, Aug 10 2017

nonn

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

Cf. A000040, A053184, A053182, A065508, A091567, A236056.

select(p -> isprime(p) and not ormap(isprime, [p^2+p+1,p^2+p-1,p^2-p+1,p^2-p-1]), [2,seq(i,i=3..1000,2)]); # Robert Israel, Aug 10 2017

Select[Prime[Range[1000]], ! (PrimeQ[#^2 + # + 1] || PrimeQ[#^2 + # - 1] ||PrimeQ[#^2 - # + 1] || PrimeQ[#^2 - # - 1]) &]
Select[Prime[Range[200]],NoneTrue[{#^2+#+1,#^2+#-1,#^2-#+1,#^2-#-1},PrimeQ]&] (* Harvey P. Dale, Oct 13 2024 *)

is(n) = my(v=[n^2+n+1, n^2+n-1, n^2-n+1, n^2-n-1]); for(k=1, #v, if(ispseudoprime(v[k]), return(0))); 1
forprime(p=1, 900, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Aug 10 2017

Intersection of the complements of A053184, A053182, A065508, and A091567 within the primes A000040.

A352604 Primes p such that p^2+3*p+1 and p^2+p-1 are also prime.

Original entry on oeis.org

2, 3, 5, 19, 53, 59, 163, 263, 349, 373, 419, 449, 499, 1013, 1093, 1259, 1303, 1423, 1489, 1493, 1669, 1759, 2069, 2729, 2879, 3463, 3943, 4159, 4243, 4283, 4493, 4603, 4793, 4969, 5113, 5303, 5563, 6323, 6599, 6803, 6829, 6883, 7369, 7523, 7529, 7963, 8039, 8713, 8969, 9043, 9173, 9293, 9623

Offset: 1

J. M. Bergot and Robert Israel, Mar 22 2022

nonn

Primes p such that (p-1)*p+(p-1)+p and p*(p+1)+p+(p+1) are also prime.

			a(3) = 5 is a term because 5, 5^2+3*5+1 = 41 and 5^2+5-1 = 29 are all prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Intersection of A053184 and A153590.

select(t -> isprime(t^2+3*t+1) and isprime(t^2+t-1), [seq(ithprime(i),i=1..10000)]);

from itertools import islice
from sympy import isprime, nextprime
def agen():
    p = 2
    while True:
        if isprime(p**2 + 3*p + 1) and isprime(p**2 + p - 1):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 53))) # Michael S. Branicky, Mar 22 2022

A154941 Sophie Germain primes in A154939.

Original entry on oeis.org

3, 5, 11, 131, 419, 1409, 2069, 3449, 3761, 3911, 6899, 7079, 7151, 9539, 9791, 10529, 10691, 11321, 11831, 14741, 15269, 17291, 22079, 27281, 27809, 30449, 34439, 45131, 48479, 52289, 54251, 64439, 70901, 75389, 78839, 85691, 101411, 102911

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

nonn

2*3+1=7, 5*2+1=11, ...

Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*(p+1)-p]&&PrimeQ[(p-1)*(p+1)+p],If[PrimeQ[p*2+1],AppendTo[lst,p]]],{n,8!}];lst
Select[Prime[Range[10000]],AllTrue[{2#+1,(#-1)(#+1)+#,(#-1)(#+1)-#},PrimeQ]&] (* Harvey P. Dale, Sep 21 2023 *)

A154944 Primes p such that (p-1)p(p+1)-p+2 and (p-1)p(p+1)+p-2 are primes.

Original entry on oeis.org

19, 37, 67, 151, 367, 859, 1471, 2791, 2971, 3061, 4357, 4447, 4507, 6367, 7159, 7237, 7591, 8311, 8647, 11617, 12211, 12601, 13249, 14947, 15271, 15661, 16699, 18097, 19777, 20149, 20347, 20947, 21019, 22741, 23311, 23857, 24019, 25867, 26701

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

nonn

Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A154942

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*p*(p+1)-p+2]&&PrimeQ[(p-1)*p*(p+1)+p-2],AppendTo[lst,p]],{n,8!}];lst

A155010 Primes p such that (p-a)(p+a)-+ap and (p-b)(p+b)-+bp are primes, a=2,b=3.

Original entry on oeis.org

7, 37, 587, 28703, 35677, 36857, 99367, 326707, 361687, 578167, 613573, 619007, 656407, 688783, 702203, 713467, 874823, 922027, 940573, 1045763, 1057907, 1244687, 1371157, 1419697, 1555187, 1665767, 1687187, 1687327, 1799453

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

nonn

Cf. A125272, A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A155006, A155007, A155008, A155009

lst={};Do[p=Prime[n];If[PrimeQ[(p-2)*(p+2)-2*p]&&PrimeQ[(p-2)*(p+2)+2*p]&&PrimeQ[(p-3)*(p+3)-3*p]&&PrimeQ[(p-3)*(p+3)+3*p],AppendTo[lst,p]],{n,9!}];lst
Select[Prime[Range[200000]],AllTrue[Flatten[{(#-2)(#+2)+{2#,-2#},(#-3)(#+3)+ {3#,-3#}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 26 2015 *)

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A290767 Primes p such that p^2 +/- p +/- 1 are all nonprimes.

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A352604 Primes p such that p^2+3*p+1 and p^2+p-1 are also prime.

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A154941 Sophie Germain primes in A154939.

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A154944 Primes p such that (p-1)*p*(p+1)-p+2 and (p-1)*p*(p+1)+p-2 are primes.

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A155010 Primes p such that (p-a)*(p+a)-+a*p and (p-b)*(p+b)-+b*p are primes, a=2,b=3.

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A154944 Primes p such that (p-1)p(p+1)-p+2 and (p-1)p(p+1)+p-2 are primes.

A155010 Primes p such that (p-a)(p+a)-+ap and (p-b)(p+b)-+bp are primes, a=2,b=3.