A086476
Primes p such that 32p+1 and (p-1)/32 are both prime.
Original entry on oeis.org
1889, 8609, 11489, 25889, 32609, 46049, 67169, 98849, 99809, 107873, 120929, 124193, 128033, 139169, 142433, 157793, 167393, 168353, 196193, 208673, 210209, 241313, 288929, 295073, 308129, 311009, 324449, 354209, 377633, 396833, 403553
Offset: 1
1889 is a member as (1889-1)/32 = 59 and 32*1889 + 1= 60449 are both prime.
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Prime[ Select[ Range[37063], PrimeQ[(Prime[ # ] - 1)/2^5] && PrimeQ[2^5Prime[ # ] + 1] & ]]
Select[Prime[Range[35000]],And@@PrimeQ[{32#+1,(#-1)/32}]&] (* Harvey P. Dale, Jan 23 2013 *)
A086478
Primes p such that 512p+1 and (p-1)/512 are both prime.
Original entry on oeis.org
183809, 220673, 420353, 629249, 696833, 1772033, 1904129, 2186753, 4137473, 4930049, 5575169, 6435329, 7040513, 8355329, 9405953, 9491969, 9882113, 10112513, 10373633, 11580929, 11648513, 11725313, 13209089, 13445633
Offset: 1
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Prime[ Select[ Range[957580], PrimeQ[(Prime[ # ] - 1)/512] && PrimeQ[512Prime[ # ] + 1] &]]
Select[Prime[Range[900000]],AllTrue[{512#+1,(#-1)/512},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 13 2018 *)
A085832
Smallest prime p such that both (p-1)/2^(2n-1) and 2^(2n-1)*p+1 are primes.
Original entry on oeis.org
5, 17, 1889, 21377, 183809, 83969, 40961, 79003649, 245235713, 5767169, 1004535809, 897581057, 41238396929, 13555990529, 2357400174593, 3438121320449, 12360915877889, 188188287041537, 286010462175233
Offset: 1
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f[n_] := Block[{k = 1}, While[ !PrimeQ[k] || !PrimeQ[(k - 1)/2^n] || !PrimeQ[2^n*k + 1], k += 2^n]; k]; Table[ f[n], {n, 1, 37, 2}]
Showing 1-3 of 3 results.
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