论文标题
数以百万计的佩林（Perrin）伪epporime包括一些巨人
Millions of Perrin pseudoprimes including a few giants
论文作者
论文摘要
许多和大型佩林伪气的计算是一个挑战。这主要是由于他们的稀有性。 Perrin伪爆炸是最稀有的已知伪爆炸之一。为了计算许多如此庞大的数字，不仅需要快速算法，而且还需要了解其中大多数构建方式如何最小化了必须测试的数量。我们提出了一种用于测试Perrin pseudaprimes的快速算法，并就Perrin pseudaprimes的构建方式提出了一些想法。这导致一些仍需要证明的猜想。我们认为，我们发现了所有20位佩林伪per液中90％以上的超过90％。总体而言，我们已经能够用我们的方法计算超过900万个Perrin伪爆炸。发现的最大数字有3101位数字。与以前刚刚已知的超过100,000 perrin伪爆炸相比，这似乎是一个突破，其中最大的数字有20位。此外，我们提出了两个新的序列，这些序列根本不提供任何伪普的$ 10^9 $。
The calculation of many and large Perrin pseudoprimes is a challenge. This is mainly due to their rarity. Perrin pseudoprimes are one of the rarest known pseudoprimes. In order to calculate many such large numbers, one needs not only a fast algorithm but also an idea how most of them are structured to minimize the amount of numbers one have to test. We present a quick algorithm for testing Perrin pseudoprimes and develop some ideas on how Perrin pseudoprimes might be structured. This leads to some conjectures that still need to be proved. We think that we have found well over 90% of all 20-digit Perrin pseudoprimes. Overall, we have been able to calculate over 9 million Perrin pseudoprimes with our method, including some very large ones. The largest number found has 3101 digits. This seems to be a breakthrough, compared to the previously known just over 100,000 Perrin pseudoprimes, of which the largest have 20 digits. In addition, we propose two new sequences that do not provide any pseudoprimes up to $10^9$ at all.
