The Possible Positions of Mersenne Prim Numbers.

[Kube Prims]

# The Possible Positions of Mersenne Prim Numbers.
# The Mersenne Prime Numbers and the Column 0 and 1.

# Die möglichen Positionen von Mersenne-Primzahlen.
# Die Mersenne-Primzahlen und die Spalten 0 und 1.

# MersenneColumns16112019v4.txt
# (c) Hans-Peter Kuberna 2019
# hans-peter@kuberna.de
# SageMath 8.1

print
print "MersenneColumns16112019v4.txt"
print " (c) Hans-Peter Kuberna  2019"
print " hans-peter@kuberna.de"
print "SageMath 8.1"

p = [2,3,5,7,13,17,19,31,61,89,107,127]         # 0..11

# SageMath FxIndexKubePrim to FxZahl
def FxKubePrimZahl(FxIndexKubePrim):
 FxKubePrimSpalten = [1,7,11,13,17,19,23,29]
 FxZeile=FxIndexKubePrim//8
 FxSpalte=FxIndexKubePrim-(FxZeile*8)
 FxZahlKubePrim=(FxZeile*30)+FxKubePrimSpalten[FxSpalte]
 return FxZeile,FxSpalte,FxZahlKubePrim
 #return FxZahlKubePrim 

FxKubePrimArray=[0,0,0]
KubePrim=FxKubePrimArray[2]

# FxKubePrimArray=FxKubePrimZahl(FxIndexKubePrim)

def FxZahlZuIndexKubePrim(FxZahlKubePrim):
 FxKubePrimSpalten = [1,7,11,13,17,19,23,29]
 FxKubePrimSpaltenArray = [0..29]
 for IndexKubePrimSpalten in range (0,29):
  FxKubePrimSpaltenArray[IndexKubePrimSpalten]=-1
 for IndexKubePrimSpalten in range (0,8):
  FxKubePrimSpalte=FxKubePrimSpalten[IndexKubePrimSpalten]
  FxKubePrimSpaltenArray[FxKubePrimSpalte]=IndexKubePrimSpalten
 FxIndexKubePrimInt30=FxZahlKubePrim//30
 FxIndexKubePrimInt30m30=FxIndexKubePrimInt30*30
 FxZahlKubePrimRest=FxZahlKubePrim-FxIndexKubePrimInt30m30
 if FxKubePrimSpaltenArray[FxZahlKubePrimRest]==-1:
  FxIndexKubePrim=-1
 else:
  FxIndexKubePrim=FxIndexKubePrimInt30*8
  FxKubePrimSpalte=FxKubePrimSpaltenArray[FxZahlKubePrimRest]
  FxIndexKubePrim=FxIndexKubePrim+FxKubePrimSpalte
 return FxIndexKubePrim  # -1 => Fehler

# ZahlZuIndexKubePrim=FxZahlZuIndexKubePrim(KubePrim)

print "--------------------------------------------",
print "--------------------------------------------"

SchleifeIndexMin=0 ; SchleifeIndexMax=8*4+1
SchleifeIndex=SchleifeIndexMin
while SchleifeIndex<=SchleifeIndexMax:
 Exponent2=SchleifeIndex

 FxKubePrimArray=FxKubePrimZahl(SchleifeIndex)
 Exponent2=FxKubePrimArray[2]
 
 #print('%21s %3s' % ("Exponent 2 =",Exponent2)),
  
 print('%21s' % ("Exponent 2 = ")),
 #print('%4s %3s' % ("Exponent2 = ")),
 print('%11s' % Exponent2),
 if is_prime(Exponent2):
  print " prime  ",
 else:
  print " not prime  ",
 print('%18s %5s' % ("Berechnung Nr. ",SchleifeIndex))

 MersennePrim=(2**Exponent2)-1
 print('%21s %22s' % ("Mersenne Prim =","(2**Exponent2)-1"))
 print('%21s %60s' % ("Mersenne Prim =",MersennePrim)),

 if is_prime(MersennePrim):
  print " prime"
 else:
  print " not prime"

 print
 IndexMersenneKubePrim=FxZahlZuIndexKubePrim(MersennePrim)
 print('%21s %60s' % ("IndexKubePrim =",IndexMersenneKubePrim)),
 if is_prime(IndexMersenneKubePrim):
  print " prime"
 else:
  print " not prime"

 FxKubePrimArray=FxKubePrimZahl(IndexMersenneKubePrim)
 KubePrim1=FxKubePrimArray[2]
 ZahlZuIndexKubePrim=FxZahlZuIndexKubePrim(KubePrim1)
 print('%21s %60s' % ("Kube Prim 1 =",KubePrim1)),
 if is_prime(KubePrim1):
  print " prime"
 else:
  print " not prime"

 KubePrimSpalte1=FxKubePrimArray[1]
 print('%21s %60s' % ("Kube Prim Spalte 1 =",KubePrimSpalte1)),
 if MersennePrim==KubePrim1:
  print " Mersenne ?  True"
 else:
  print " Mersenne ?  False"

 print
 IndexMersenneKubePrim=FxZahlZuIndexKubePrim(MersennePrim)
 IndexMersenneKubePrimPlus1=IndexMersenneKubePrim+1
 print('%21s %60s' % ("IndexKubePrim+1 =",IndexMersenneKubePrimPlus1)),
 if is_prime(IndexMersenneKubePrimPlus1):
  print " prime"
 else:
  print " not prime"

 FxKubePrimArray=FxKubePrimZahl(IndexMersenneKubePrimPlus1)
 KubePrim2=FxKubePrimArray[2]
 ZahlZuIndexKubePrim=FxZahlZuIndexKubePrim(KubePrim2)
 print('%21s %60s' % ("Kube Prim 2 =",KubePrim2)),
 if is_prime(KubePrim2):
  print " prime"
 else:
  print " not prime"

 KubePrimSpalte2=FxKubePrimArray[1]
 print('%21s %60s' % ("Kube Prim Spalte 2 =",KubePrimSpalte2)),
 if MersennePrim==KubePrim2:
  print " Mersenne ?  True"
 else:
  print " Mersenne ?  False"

 SchleifeIndex=SchleifeIndex+1
 print "--------------------------------------------",
 print "--------------------------------------------"
print