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##############################################################################
##
#A generateCANFACT.g Frank Lübeck
##
## This file can be read by GAP to produce an update of the list 'CANFACT' in
## 'CANFACT.g'. For example after an update of the list of Brent factors, see
## '?FetchMoreFactors'.
##
## The idea is to fork GAP instances which try for 5 seconds to factorize p^n
## - 1. If successful the pair (p,n) is included in CANFACT.
##
SetInfoLevel( InfoPrimeInt, 0 );
out := OutputTextFile("CANFACT", false);
SetPrintFormattingStatus(out, false);
AppendTo(out, "CANFACT := [];\n");
for p in Filtered([1..10000], IsPrime) do
Print(p," [\c");
if p < 10 then
max := 2000;
elif p < 100 then
max := 500;
else
max := 100;
fi;
AppendTo(out, "CANFACT[",p,"]:=[];\n");
l := [];
for n in [1..max] do
Print([p,n]," \c");
pf := ParTakeFirstResultByFork([Factors],[[p^n-1]],
rec(TimeOut:=rec(tv_sec:=5,tv_usec:=0)));
if Length(pf) > 0 then
AppendTo(out, "Add(CANFACT[",p,"],",n,");\n");
fi;
od;
od;
CloseStream(out);
Print("""Read the file 'CANFACT' and print the variable CANFACT to the file
CANFACT.g
to store the data more compactly.
""");
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