A048880
Primes of form pq+2 where p and q are consecutive primes.
Original entry on oeis.org
17, 37, 79, 223, 439, 4759, 22501, 32401, 53359, 57601, 60493, 72901, 77839, 95479, 99223, 159199, 164011, 176401, 194479, 239119, 324901, 378223, 416023, 497011, 680623, 756853, 804511, 1115113, 1664101, 1742401, 2223079
Offset: 1
Herman H. Rosenfeld (herm3(AT)pacbell.net)
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with (numtheory): for n from 1 to 1000 do if (tau(ithprime(n)*ithprime(n+1)+2)=2) then print(ithprime(n),ithprime(n+1),ithprime(n)*ithprime(n+1)+2); fi; od;
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Reap[Do[If[PrimeQ[p=Prime[k]*Prime[k+1]+2],Sow[p]],{k,1,430}]][[2,1]] (* Zak Seidov Dec 03 2010 *)
Corrected and extended by Joe DeMaio (jdemaio(AT)kennesaw.edu).
A342565
Numbers k such that 6*k - 1 is a prime that can be written as p*q - 2, with p and q being consecutive primes.
Original entry on oeis.org
4265, 7842, 11265, 22815, 52265, 160065, 167662, 322003, 383542, 393722, 1016815, 1051677, 1150182, 1290842, 1372803, 1555498, 1826015, 2184065, 2808498, 3168265, 3200307, 3231062, 3333117, 3427680, 3676962, 3913915, 4042598, 4323102, 4537907, 4623542, 4798955
Offset: 1
a(1) = 4265, because the prime 25589 = 6*4265 - 1 can be written as 157*163 - 2, with 157 and 163 being consecutive primes.
Cf.
A123921, whose first term 13 = 3*5 - 2 cannot be written as 6*k - 1.
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a342565(plim)={my(p1=5);forprime(p2=7,plim,my(p=p1*p2-2);if(isprime(p),print1((p+1)/6,", "));p1=p2)};
a342565(5400)
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from primesieve.numpy import n_primes
from numbthy import isprime
primesarray = numpy.array(n_primes(10000, 1))
for i in range (0, 9999):
totest = int(primesarray[i] * primesarray[i+1] - 2)
if (isprime(totest)) and (((totest+1)%6) == 0):
print((totest+1)//6) # Karl-Heinz Hofmann, Jun 20 2021
Showing 1-2 of 2 results.
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