双语畅销书《艾伦图灵传》第9章:退隐山林(14)
Another change was that each line on the cathode ray tube store now held forty spots, an instruction taking up twenty of them.
These were conveniently thought of as grouped in fives, and a sequence of five binary digits as forming a single digit in the base of 32.
每5个点被划分成一组，存储5个二进制位，表示一个32进制的数字。Meanwhile Newman made an ingenious choice of problem with which to demonstrate the machine.
但在演示这台机器时，纽曼选择了一个很不明智的例子。
as it stood with only a tiny store but with a multiplier, it was something that had been discussed at Bletchley-finding large prime numbers.
这台机器的存储容量还非常小，但纽曼选择了一个在布莱切利曾经讨论过的问题——寻找大素数。In 1644, the French mathematician Mersenne had conjectured that 217-1, 219-1, 231-1, 267-1, 2127-1, 2257-1 were all prime, and that these were the only primes of that form within the range.
在1644年，数学家推测217-1、219-1，231-1，267-1，2127-1，2257-1（图，平方号，后面还有）都是素数，而且是这个范围内仅有的这种形式的素数。In the eighteenth century, Euler laboriously established that 231 - 1 = 2, 146, 319, 807 was indeed prime, but the list would not have progressed further without a fresh theory.
到了18世纪，欧拉艰难地证明了231-1=2，146，319，807确实是个素数，但如果没有新的理论来支撑，这种方法无法走得更远。In 1876, the French mathematician E. Lucas proved that there was a way to decide whether 2p-1 was prime by a process of p operations of squaring and taking of remainders, He announced that 2127-1 was prime.
1876年，法国数学家E·卢卡斯提出，可以通过一系列关于p的运算来检验2p-1是否是素数，并证明了2127-1是素数。In 1937, the American D.H. Lehmer attacked 2257-1 on a desk calculator and after a couple of years of work showed that Mersenne had been mistaken.
1937年，美国的D·H·莱默利用台式计算器证明了2257-1是素数, 接下来几年的工作表明，梅森的猜想是错误的。In 1949, Lucas's number was still the largest known prime, Lucas's method was tailor-made for a computer using binary numbers.
直到1949年，卢卡斯的素数依然是人们所知的最大素数，卢卡斯的方法是专门为二进制计算机设计的。They had only to chop up the huge numbers being squared into 40-digit sections and to program all the carrying.
所以他们需要做的工作，只是把大数分割成40位的小块，以便于存储。Newman explained the problem to Tootill and Kilburn, and in June 1949, they managed to pack a program into the four cathode ray tubes and still leave enough space for working up to P = 353.
纽曼给托蒂尔和吉尔博解释了这个问题，并且在1949年6月，他们成功地做到，在加载了程序之后，仍有足够的空间来处理p小于353时的所有情形。En route they checked all that Euler and Lucas and Lehmer had done, but did not discover any more primes.
他们检查了欧拉、卢卡斯和莱默的所有工作，但却没能找到更大的素数注。
