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A007510 Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.
(Formerly M2130)
78
2, 23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 157, 163, 167, 173, 211, 223, 233, 251, 257, 263, 277, 293, 307, 317, 331, 337, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 509, 541, 547, 557, 563 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Almost all primes are a member of this sequence by Brun's theorem.

A010051(a(n))*(1-A164292(a(n))) = 0; complement of A001097 with respect to A000040. [From Reinhard Zumkeller, Mar 31 2010]

REFERENCES

Richard L. Francis, "Isolated Primes", J. Rec. Math., 11 (1978), 17-22.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Yahoo! Groups, PrimeForm e-group

Wikipedia, Isolated prime

MAPLE

with(numtheory): for i from 1 to 150 do p:=ithprime(i): if(not isprime(p+2) and not isprime(p-2)) then printf("%d, ", p) fi od: (Pab Ter)

A007510 := proc(n) if n = 1 then 2; else for a from procname(n-1)+1 do if isA007510(a) then return a; end if; end do; end if; end proc:

isA007510 := proc(n) isprime(n) and not isprime(n+2) and not isprime(n-2) ; simplify(%) ; end proc:  # R. J. Mathar, Apr 26 2010

MATHEMATICA

Transpose[Select[Partition[Prime[Range[100]], 3, 1], #[[2]] - #[[1]] != 2 && #[[3]] - #[[2]] != 2 &]][[2]] - Harvey P. Dale Mar 01 2001

Select[Prime[Range[4, 100]], !PrimeQ[ #-2]&&!PrimeQ[ #+2]&] (* Zak Seidov May 07 2007 *)

PROG

UBASIC: 10 'primes using counters 20 N=3:print "2 "; :print "3 "; :C=2 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 55 55 Q=N+2:R=N-2: if Q<>prmdiv(Q) and N=prmdiv(N) and R<>prmdiv(R) then print Q; N; R; "-"; :stop:else N=N+2:goto 30 60 A=A+2 70 if A<=sqrt(N) then 40:stop 81 C=C+1 100 N=N+2:goto 30 - Enoch Haga, Oct 08 2007

(PARI) forprime(x=2, 1000, if(!isprime(x-2)&&!isprime(x+2), print(x))) [From Zak Seidov, Mar 23 2009]

CROSSREFS

Cf. A083370 A124582 A134099 A134100 A134101.

Sequence in context: A049580 A061448 A115233 * A117242 A144550 A106736

Adjacent sequences:  A007507 A007508 A007509 * A007511 A007512 A007513

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 11 2005

STATUS

approved

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Last modified April 16 06:49 EDT 2014. Contains 240549 sequences.