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A235364 Twin primes p, p+2 such that p+1 is a Giuga number. 2
29, 31, 857, 859, 1721, 1723 (list; graph; refs; listen; history; text; internal format)



For all 12 known Giuga numbers N, either both N-1 and N+1 are prime or neither is prime. Is it true that if any Giuga number N is adjacent to a prime N-1 or N+1, then in fact N lies between twin primes N-1, N+1?

See A235139 for a similar property of the known primary pseudoperfect numbers.

A007850 lists a 13th in its comments. - Bill McEachen, Jan 14 2014

If g = 420001794970774706203871150967065663240419575375163060922876441614\ 2557211582098432545190323474818 is confirmed as the 13th Giuga number, it will not be between a(7) and a(8), because g-1 is divisible by 13. So a(7) is not equal to g-1. But g+1 is prime (certified using the APRCL test in Pari) so g provides a negative answer to the above question. - Ralf Stephan, Jan 20 2014 (corrected by Jonathan Sondow, Jan 21 2014)

(Revision of my question.) For all 13 known Giuga numbers N, if N-1 is prime, then N+1 is also prime. Is it true that if any Giuga number N is 1 more than a prime, then N lies between twin primes N-1, N+1? - Jonathan Sondow, Mar 02 2014


Table of n, a(n) for n=1..6.

MathWorld, Giuga Number

Wikipedia, Giuga number


For the twin primes (p,p+2) = (29, 31), (857, 859), (1721, 1723), the numbers p+1 = 30, 858, 1722 are Giuga numbers (A007850).


Cf. A007850, A235139.

Sequence in context: A288615 A158342 A077286 * A178425 A294737 A261521

Adjacent sequences:  A235361 A235362 A235363 * A235365 A235366 A235367




Jonathan Sondow, Jan 07 2014



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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)