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Prodigy's partner in Mobb Deep thought his death was one of those rumors they hear all the time, and he even joked around about it ... until he confirmed the devastating news hours later.

Havoc spoke out for the first time since Prodigy died, and told us he left Las Vegas Sunday knowing Prodigy was in the hospital. Unfortunately, that wasn't uncommon and Havoc says he wasn't too concerned -- his friend had battled sickle cell throughout their 28 years together. Plus, he'd checked up on him multiple times by phone ... and his condition was improving.

Havoc thought nothing of a "weird rumor" he heard Tuesday morning, saying ... "I was really laughing, to be honest with you."

One call to their road manager changed that.

Havoc says he made the call while driving from his 5-year-old son's kindergarten graduation -- "I could've crashed with my kids in the car."