Thursday, May 05, 2011

[aphowoil] Prime day frequency thresholds

Let a Prime Day be a day at which you have lived a prime number of days.  By the celebrated Prime Number Theorem, we have the following results: By age 9 (e^8 = 2981 days), the average spacing between Prime Days exceeds 8 days.  By age 23 (e^9 = 8103 days), the average spacing exceeds 9 days.  By age 61 (e^10 = 22,026 days) the average spacing exceeds 10 days.

The ages kind of mark thresholds in life.

Also, on your 86th birthday, you are in the midst of a very long stretch of composite days (72 days, a record prime gap).

Gap length in daysAge in daysAge in years
3413273.6331279945243
32559115.3073237508556
34846723.1813826146475
36955126.1492128678987
34997327.3045859000684
321079929.5660506502396
341174332.1505817932923
341216333.3004791238877
361285335.1895961670089
361410738.6228610540726
441568342.9377138945927
361582343.3210130047912
421614144.1916495550992
341725747.2470910335387
361880351.4798083504449
341908752.2573579739904
401933352.9308692676249
521960953.6865160848734
342044355.9698836413415
402080956.9719370294319
342143358.6803559206023
362219360.7611225188227
362230761.0732375085558
402257361.8015058179329
362281762.4695414099932
362428166.4777549623546
402526169.160848733744
522547169.7357973990418
362714374.3134839151266
322770175.8412046543463
322785176.2518822724162
482822977.2867898699521
362835177.6208076659822
342968381.2676249144422
362988181.8097193702943
383059383.7590691307324
723139785.9603011635866

A002386

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