acc:=1000
j1:=99
j2:=j1+7
m=2 ;
p:=2*x+1
sol:=N[Sinh[p*ArcSinh[m]] , acc]
sol1:=Rationalize[sol]
sol2:=sol1-m
ratio:=sol2/p
ask1:=IntegerQ[ratio]
Table[PrimeQ[p] , {x,j1,j2}]
Table[ask1 , {x,j1,j2}]
{True, False, False, False, False, False, True, False}
{True, False, False, False, False, False, True, False}