prime.rb

def sqrt(a)
  begv = 1
  endv = a
  while endv > begv + 1
     mid = (endv + begv)/2
     if mid ** 2 <= a
        begv = mid
     else
        endv = mid
     end
  end
  return begv 
end

N1 = 179769313486231590772930519078902473361797697894230657273430081157732675805505620686985379449212982959585501387537164015710139858647833778606925583497541085196591615128057575940752635007475935288710823649949940771895617054361149474865046711015101563940680527540071584560878577663743040086340742855278549092581

a1 = sqrt(N1)+1
x1 = sqrt(a1*a1 - N1)

p1 = a1 - x1
q1 = a1 + x1

puts "p_1 = #{p1}"
puts "q_1 = #{q1}"

N2 = 648455842808071669662824265346772278726343720706976263060439070378797308618081116462714015276061417569195587321840254520655424906719892428844841839353281972988531310511738648965962582821502504990264452100885281673303711142296421027840289307657458645233683357077834689715838646088239640236866252211790085787877

(sqrt(N2)..N2).each do |a2|
	x2 = sqrt(a2*a2 - N2)
	p2 = a2 - x2
	q2 = a2 + x2
	if (p2*q2-N2) == 0 then
		puts "p_2 = #{p2}"
		puts "q_2 = #{q2}"
		break
	end
end