Prime Numbers Research

This Chrome Extension is designed to check if a number is a Prime Number using the Miller-Rabin primality test, and allows research across a range of numbers. Those studying or interested in Number Theory, Cryptography, Computer Science or Data Analysis should have fun with this tool. Not only will it allow you to explore the properties of Prime Numbers using different values of the K Factor (number of iterations), but for more advanced students it will give an insight into the Miller Rabin primality test, and at the same time it will help develop skills in using a spreadsheet to analyse the resulting data. The Miller-Rabin primality test is a probabilistic algorithm used to determine whether a number is prime. It works by repeatedly checking whether a number behaves like a prime under certain conditions. If a number passes all tests, it's likely prime, but if it fails any, it's definitely composite. The test is efficient and often used for large numbers in cryptography. By adjusting the number of iterations (K Factor), the test's accuracy can be increased, with more iterations providing a higher probability of correctness. The confidence level in the Miller-Rabin primality test depends on the number of iterations (or rounds) performed. Each iteration reduces the probability of a false positive (incorrectly classifying a composite number as prime). - After one iteration, the probability of a false positive is at most 1/4 (25%). - After k iterations, the probability of a false positive is reduced to (1/4)^k. - For example, with 10 iterations, the probability of a false positive is (1/4)^10 = 1/1048576 ≈ 0.000095%. The K Factor can be changed using the slider (From 1 to 30), and the corresponding Confidence Level (1 - probability of false positive) will be shown as the K Factor changes. The default is set to 10. Use this Extension as follows: Enter a number to check if it is a Prime Number, and click the appropriate button. This will also report if a Prime Number is a Twin with a Prime Number preceding or following it. Use the range feature to check multiple numbers, and then place the results into the Clipboard. Click the appropriate button to initiate. To keep the processing time short, the maximum count that can be input is 30,000 numbers. The Count ignores Even numbers, except for the number 2. To research more than 30,000 numbers, this can be done in multiple chunks. The Clipboard will contain a heading (which will include the K Factor used) in the first row, and then a row per number in a comma-delimited format showing: Number & whether Prime (Y for Yes, N for No). The contents of the Clipboard can then be copied into a spreadsheet such as Microsoft Excel, Apple Numbers, Google Sheets, or another application of your choice. When pasting into a spreadsheet, different spreadsheets will treat the data differently. For example, Apple Numbers will automatically split the data into columns, but Microsoft Excel may require you to use the Text to Columns feature, and Google Sheets the Split to Column feature, both features found under the Data menu item. Also, very large numbers are allowed, and could be shown in scientific notation in some spreadsheets, and so these will need to be converted to text to show the full number. Once the data is in the spreadsheet, there will be very many ways that you can then use the data to create charts, graphs, and other visual representations to help you understand the data. For example, you could create a pie chart to show the percentage of Prime Numbers in the range, or look at the distribution of the gaps between Prime Numbers. By Copying & Pasting the results of different K Factors into the same spreadsheet, the different accuracies can be inspected. This tool is a great way to introduce students to the concept of data analysis and the use of spreadsheets. Clicking on the logo will show the version of the Extension. Please note that the popup window can be resized and moved around. To close the popup, click the Close Prime Numbers Research button. Enjoy Prime Numbers Research, and you never know, you may discover some very interesting insights, but whatever else, have fun! This extension is free of fees and adverts. Privacy User data is not collected or processed.