The computer whizz - the world's second richest man - called on geeks to use technology to improve rubber contraceptives.
His charity is offering a $100,000 (£66,000) start-up grant to anyone who can create a condom better than the latex sheaths used by punters today.
Further funding of a million dollars - £660,000 - could follow to develop the best idea.
The Bill & Melinda Gates Foundation's call for a Condom 2.0 is part of its Grand Challenges Explorations initiative, a grant programme aimed at funding projects that improve the lives of the world's poor.
Though condoms are cheap and reliable, too many men think they spoil the fun - leading to unwanted pregnancies and the devastating spread of disease, the foundation says.
Stephen Ward, a programme officer for the foundation, said: "We acknowledge that we have condoms today that are very effective. But they have a drawback, where they have diminished sexual pleasure for the user.
"It may seem like a small thing, but it prevents people from using them consistently. The more we can get people to be more consistent, the better."
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