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Take for example a custard. I recall reading somewhere, probably on the internet, that heating it to 70C will kill all the bacteria in it for sure. I also recall reading that holding it for 5 minutes at 60C will do the same thing.

I’m having trouble finding a proper reference for this. Is what I said actually true? It must have been studied in food science, so is there a proper source for this?

Kirill
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According to J.D. Schuman, info that I found in Douglas Baldwin's guide for sous-vide:

Place egg in a 135°F (57°C) water bath for at least 1 hour and 15 minutes (Schuman et al., 1997).

J. D. Schuman, B. W. Sheldon, J. M. Vandepopuliere, and H. R. Ball, Jr. Immersion heat treatments for inactivation of Salmonella enteritidis with intact eggs. Journal of Applied Microbiology, 83:438–444, 1997.

This is for whole eggs in the shell, so for your custard the time should vary according to the volume (as it will take longer for the temperature to reach the center).

Here is a time table for Salmonella reduction from The Modernist Cuisine (by Nathan Myrvold):

enter image description here

Luciano
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Bear in mind, it is the product temperature and Not the oven temperature. It will take a while for the product temperature to rise up. Once it reaches 60C, you still have to hold it for another 12 min on top of it.