{"id":3850,"date":"2022-09-14T14:25:28","date_gmt":"2022-09-14T12:25:28","guid":{"rendered":"https:\/\/erlebnisland-mathematik.de\/?page_id=3850"},"modified":"2023-11-10T13:07:28","modified_gmt":"2023-11-10T12:07:28","slug":"deepening-text-factor-clock","status":"publish","type":"page","link":"https:\/\/erlebnisland-mathematik.de\/en\/deepening-text-factor-clock\/","title":{"rendered":"Advanced text factor clock"},"content":{"rendered":"

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Factor Clock<\/h1>\n

The factor clock<\/em> displays the time in the form \"\mathrm{Stunden:Minuten:Sekunden}\", that is, as \"\mathrm{hh:mm:ss}\", and then decomposes the number \"\mathrm{hhmmss}\" into prime factors<\/em>. For example, a quarter of an hour past eleven, that is, at 11:15:00, the following is displayed: \"111500=2\cdot 2\cdot 5\cdot 5\cdot 223\". The somewhat strange idea of reading the time (including seconds) as a decimal number and then factorizing it goes back to the Internet comic series xkcd<\/em>, see Figure 1 below:[\/vc_column_text][vc_single_image image=”1554″ img_size=”large” alignment=”center”]Figure 1: The deciding xkcd comic (license xkcd, Creative Commons)[\/vc_single_image][vc_column_text]<\/p>\n

And now … the mathematics:<\/h3>\n

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Part 1: Facts<\/h4>\n

Because \"\mathrm{hh}<24\", \"\mathrm{mm}<60\" and \"\mathrm{ss}<60\" must apply, not all of the 1000000 six-digit numbers occur, but only as many as the day has seconds, namely 86400. Among them are 7669 prime numbers. The last prime time before midnight is 23:59:51. The number 235951 is number 20903 among all prime numbers, but only number 7669 among factor clock primes. However, the majority of the 7669 prime numbers that the factor clock can display will not be seen by visitors to the MATHS ADVENTURE LAND because they are outside the museum’s opening hours:<\/p>\n