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A090695 Integers which are not the sum of 2 integers A and B with AB+1 and AB-1 both primes. In other words, the product cannot be the middle integer of a Twin Prime pair. 4

%I #9 Oct 31 2017 06:36:52

%S 1,2,3,6,10,12,14,15,20,26,30,40,45,54,60,66,75,80,90,100,105,117,120,

%T 150,180,250,270,280,290,315,320,342,360,390,410,432,440,450,455,480,

%U 495,510,540,560,590,630,645,765,810,980,1080,1170,1220,1305,1430,1530,1860,2235,2310,2670,3120

%N Integers which are not the sum of 2 integers A and B with AB+1 and AB-1 both primes. In other words, the product cannot be the middle integer of a Twin Prime pair.

%C Sequence may be finite. Next term after 3120 if it exists must be greater than 867750.

%C If the sequence can be proved to be finite, then one may surmise that there are infinitely many twin primes and that every integer greater than 3120 and every prime, except 2 and 3, is the sum of 2 integers whose product is the middle number of a twin prime pair.

%C If there is a term after 3120, it is larger than 4*10^9. - _Giovanni Resta_, Oct 31 2017

%e 15 is a member: 15 is the sum of these pairs of integers: (2+13) (3+12) (4+11) (5+10) (6+9) (7+8). Their products (2*13) (3*12), etc. plus and minus 1 are not primes and therefore the products cannot be the middle integers of Twin Prime sets.

%o (PARI) isok(n) = {for (a=1, n\2, ab = a*(n-a); if (isprime(ab+1) && isprime(ab-1), return (0));); return (1);} \\ _Michel Marcus_, Jul 12 2013

%Y Cf. A014574, A091182, A091183.

%K nonn,fini

%O 1,2

%A William F. Sindelar (w_sindelar(AT)juno.com), Dec 19 2003

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)