欧拉计划808：可反转质数平方

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发现一个规律，不知道能否证明，x平方的逆序开方恰好等于x的逆序

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newkid 发表于 2022-10-30 10:17
以前有个帖子用PLSQL筛法构造素数表，我找不到了。但是估计这个素数表也不够大，凑不出50个。

后面比较稠密
pe的题目一般答案<Uint64，所以x<Uint32就可以了

solomon_007

〇〇 发表于 2022-10-30 14:01
发现一个规律，不知道能否证明，x平方的逆序开方恰好等于x的逆序

17^2 = 289     ->    982 <> 71^2     不成立

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solomon_007 发表于 2022-10-30 22:48
17^2 = 289     ->    982  71^2     不成立

我是说本题的可翻转质数

jihuyao

It looks such a number is so scattered so I am wondering what is the probability it occurs , say within all three-digit number between 100 and 1000 (since it is a 10 based number problem.  To make it as simple as possible, there are (1000-100)/6=150 6k+1 and 150 6k-1 candidates.  Assuming each may have one factor 5/7/11/13/17/19/23/25, the probability of each candidate being prime is 1/9.  Then consider those among 150 eligible being reversed, {1,3,7,9} / {1,2,3,4,5,6,7,8,9} => 4/9.  Then consider after being powered by 2, 1**2=> 1(only take first digit as the last digit after being reversed), 3**2 =>9, 7**2=> 4, 9**2=>8.  So only half may be eligible after **2 and reversed.  The probability is about 1/9*4/9*1/2.  So the within all three digit number, 300*1/9*4/9*1/2= 7 may be obtained.  Of cause, this is too much simplified.  But the trend (I guess) is for increasing digits range, the probability is decreased.  Maybe we can use calculus to make a little better estimate?