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 *)
A086477
Primes p such that 128p+1 and (p-1)/128 are both prime.
Original entry on oeis.org
21377, 44417, 140417, 151169, 151937, 155777, 436097, 539009, 569729, 570497, 608129, 658817, 704897, 830849, 865409, 965249, 1000577, 1008257, 1054337, 1130369, 1214849, 1311617, 1419137, 1429889, 1556609, 1618817, 1779329
Offset: 1
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Prime[ Select[ Range[141120], PrimeQ[(Prime[ # ] - 1)/2^7] && PrimeQ[2^7Prime[ # ] + 1] & ]]
Select[Prime[Range[140000]],AllTrue[{128#+1,(#-1)/128},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 13 2019 *)
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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