Jelly, 16 bytes
ÆRḤ‘$ÆP$Ƈ’H$ÆP$Ƈ
ÆR - list of prime numbers up to the input
Ḥ‘ - 2x+1
$ÆP$Ƈ - evaluates as primes
’H - (x-1)/2
$ÆP$Ƈ - evaluates as primes (again)
Jelly, 16 bytes
ÆRḤ‘$ÆP$Ƈ’H$ÆP$Ƈ
ÆR - list of prime numbers up to the input
Ḥ‘ - 2x+1
$ÆP$Ƈ - evaluates as primes
’H - (x-1)/2
$ÆP$Ƈ - evaluates as primes (again)