Vuonna 1849 Gauss kirjoitti astronomi Johan Franz Enckelle vastauksessaan Encken kommentteihin alkulukujen esiintymistiheydestä:
“Most Honored Friend! . . .The kind communication of your remarks on the frequency of prime numbers was interesting to me in more than one respect. You have reminded me of my own pursuit of the same subject, whose first beginnings occurred a very long time ago, in 1792 or 1793, when I had procured for myself Lambert’s supplement to the table of logarithms. Before I had occupied myself with the finer investigations of higher arithmetic, one of my first projects was to direct my attention to the decreasing frequency of prime numbers, to which end I counted them up in several chiliads (sets of a thousand) and recorded the results on one of the affixed white sheets. I soon recognized, that under all variations of this frequency, on average, it is nearly inversely proportional to the logarithm…”
Gauss ei koskaan julkaissut tuloksiaan. Ensimmäinen julkaistu versio alkulukuteoreemasta on Legenderen käsialaa vuodelta 1798.