雙語暢銷書《艾倫圖靈傳》第9章:退隱山林(14)

Another change was that each line on the cathode ray tube store now held forty spots, an instruction taking up twenty of them.

另一項改變是，現在每條陰極射線管組成的“線”可以存儲40個點，每條指令佔用20個點。

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個點被劃分成一組，存儲5個二進制位，表示一個32進制的數字。

Meanwhile Newman made an ingenious choice of problem with which to demonstrate the machine.

但在演示這臺機器時，紐曼選擇了一個很不明智的例子。

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.

這臺機器的存儲容量還非常小，但紐曼選擇了一個在布萊切利曾經討論過的問題——尋找大素數。

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，數學家推測217-1、219-1，231-1，267-1，2127-1，2257-1（圖，平方號，後面還有）都是素數，而且是這個範圍內僅有的這種形式的素數。

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世紀，歐拉艱難地證明了231-1=2，146，319，807確實是個素數，但如果沒有新的理論來支撐，這種方法無法走得更遠。

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，法國數學家E·盧卡斯提出，可以通過一系列關於p的運算來檢驗2p-1是否是素數，並證明了2127-1是素數。

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，美國的D·H·萊默利用臺式計算器證明了2257-1是素數, 接下來幾年的工作表明，梅森的猜想是錯誤的。

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，盧卡斯的素數依然是人們所知的最大素數，盧卡斯的方法是專門爲二進制計算機設計的。

They had only to chop up the huge numbers being squared into 40-digit sections and to program all the carrying.

所以他們需要做的工作，只是把大數分割成40位的小塊，以便於存儲。

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.

紐曼給托蒂爾和吉爾博解釋了這個問題，並且在1949年6月，他們成功地做到，在加載了程序之後，仍有足夠的空間來處理p小於353時的所有情形。

En route they checked all that Euler and Lucas and Lehmer had done, but did not discover any more primes.

他們檢查了歐拉、盧卡斯和萊默的所有工作，但卻沒能找到更大的素數注。