在 Livecode 中生成并检查非常大数的素数

Question

我该怎么做？这些产生语言的所有其他结果不是 LiveCode 或由于某种原因在 LiveCode 中不起作用。数字必须随机生成；否则，我可以从here 中取一些（是的，~150 位数）。最终目标是将这些用于加密（个人实验）。

Answer 1

你没有说到目前为止你做了什么。生成大素数的基本方法是：

repeat
  pick a large possible prime
until (the number you picked is prime)

那是伪代码，因为我不知道 LiveCode。您必须自己进行转换。

所有大素数的形式为 6n ± 1。您可以根据所需的素数大小在合适的范围内选择 n。

对于素数测试，您必须将标准素数测试之一转换为 LiveCode。或者，有没有办法将其他语言的外部方法合并到 LiveCode 中，这样您就可以从网络上复制一个示例？

Answer 2

我们在这里谈论多大？大多数编程语言都使用标准数字类型在内部存储数字，这些数字具有固定大小（例如，4 个字节为您提供大约 -20 亿到 +20 亿之间的数字）。

因此他们不太可能处理 150 位数字。

您可能必须获得一个 LiveCode 插件（外部？无论 LiveCode 使用什么来称呼它们），它可以处理非常大的数字或执行“字符串数学”。

Answer 3

LiveCode 使用列表的 Devin Asay 先生提供了这个：

on mouseUp
 local tNum
 put fld 2 into tNum
 put "" into fld 1
 put isPrime(tNum) into fld 1
end mouseUp

function isPrime pNum
 if pNum <> 2 AND pNum mod 2 = 0 then
  return false
 end if
 repeat with x = 3 to sqrt(pNum) step 2
  if pNum mod x = 0 then
     return false
  end if
 end repeat
 return true
end isPrime

由于范围（溢出）错误，处理程序在 309 位时失败。这是机器限制，而不是 LC 限制。处理程序的整体精度是有限的（LC 团队的 Mark Waddingham 表示）：

您只能表示最大为 2^53 左右的整数而不会丢失 精度（因为它们使用 IEEE 双精度表示），这意味着 您可以使用此方法检查素数的最大数量约为 9007199254740992。

Answer 4

我可以毫无问题地处理使用 livecode 或任何其他语言的数字 long 任何数字的完全完美。我可以只使用 + - / * 操作，但我认为这对你的研究来说已经足够了。我做了这个函数：

function bigAdd a1, a2
  #let's check if it's negative...
  #end check
  put reverse2(a1) into b1
  put reverse2(a2) into b2
  put 0 into mem
  if length(b1) < length(b2) then
    put b1 into temp
    put b2 into b1
    put temp into b1
  end if
  repeat while b2 is not empty
    put (char 1 of b1) + (char 1 of b2) + mem into ppp
    if length(ppp) = 1 then
       put 0 into mem
       put ppp before rrr
   else
     put 1 into mem
     put char 2 of ppp before rrr
   end if
  delete char 1 of b1
  delete char 1 of b2
end repeat
repeat while (b1 is not empty)
put mem + (char 1 of b1) into ppp
if length(ppp) = 1 then
put 0 into mem
put ppp before rrr
else
put 1 into mem
put char 2 of ppp before rrr
end if
delete char 1 of b1
end repeat
if mem = 1 then
put 1 before rrr
else
put b1 before rrr
end if
return rrr
end bigAdd

function reverse2 temp
repeat for each char tChar in temp
put tChar before temp2
end repeat
return temp2
end reverse2


function bigMultiply a1,a2
put reverse2(a1) into a1
put 0 into temp
repeat for each char tChar in a1
repeat with i=1 to tChar
put bigAdd(temp,a2) into temp
end repeat
put 0 after a2
end repeat
return temp
end bigMultiply

function bigGreater a1,a2
#compare two bignumbers:
#return true if n1 > n2
#return false if n1 < n2
#return empty if n1 = n2
#let's check is a number is negative
if ((char 1 of a1 = "-") or (char 1 of a2 = "-")) then
if ((char 1 of a1 = "-") and (char 1 of a2 is not "-")) then
return false
end if
if ((char 1 of a1 is not "-") and ( char 1 of a2 = "-" )) then
return true
end if
#if we are here, both are negative
delete char 1 of a1
delete char 1 of a2
if a1 = a2 then
return empty
else
return (not bigGreater(a1,a2))
end if
end if
if length(a1) is not length(a2) then
return ( length(a1) > length(a2) ) #this is evalueted true or false
else
if a1 = a2 then
return empty
else
repeat while ((char 1 of a1) = (char 1 of a2) )
delete char 1 of a1
delete char 1 of a2
end repeat
return ((char 1 of a1) > (char 1 of a2)) #this is evalueted true or false
end if
end if
end bigGreater

function bigSub a1,a2
#substract the smallest big number from the largest one
if bigGreater(a2,a1) then
put a1 into temp
put a2 into a1
put temp into a2
end if
put reverse2(a1) into a1
put reverse2(a2) into a2
put 0 into mem
repeat while (a2 is not empty)
put (char 1 of a1) - mem + 10 - (char 1 of a2) into minus
if length(minus) = 1 then
put 1 into mem
put minus before rrr
else
put 0 into mem
put char 2 of minus before rrr
end if
delete char 1 of a1
delete char 1 of a2
end repeat
repeat while (a1 is not empty)
put char 1 of a1 + 10 - mem into minus
if length(minus) = 1 then
put 1 into mem
put minus before rrr
else
put 0 into mem
put char 2 of minus before rrr
end if
delete char 1 of a1
end repeat
#remove inital zeros
repeat while (char 1 of rrr is "0")
delete char 1 of rrr
end repeat
return rrr
end bigSub

function bigDivide a1,a2
#output is a block of two numbers "quotient , remainder"
if bigGreater(a2,a1) then
return ("0," & a1)
end if
if a1 = a2 then
return "1,0"
end if
put 0 into count
repeat while (bigGreater(a1,a2))
put bigSub(a1,a2) into a1
put bigAdd(1,count) into count
end repeat
if a1 = a2 then
put bigAdd(count,1) into count
put 0 into a1
end if
return (count & comma & a1)
end bigDivide

function bigDivide2 a1,a2
#please note that the result is "the result, the remainder"
put length(a1) into ldividendo
put length(a2) into ldivisore
if ldividendo <= ldivisore then
return bigDivide(a1,a2)
end if
put char 1 to ldivisore of a1 into tDiv
put bigDivide(tDiv,a2) into rrr
put item 1 of rrr into quoziente
put item 2 of rrr into resto
put ldivisore + 1 into nn
repeat with i = nn to ldividendo
put char i of a1 after resto
put bigDivide(resto,a2) into temp
put item 1 of temp after quoziente
put item 2 of temp into resto
end repeat
put removezeros(quoziente) into quoziente
put removezeros(resto) into resto
return (quoziente & comma & resto)
end bigDivide2

function removezeros temp
repeat while char 1 of temp is "0"
delete char 1 of temp
end repeat
return temp
end removezeros