I'd say the Riemann hypothesis is more famous. Goldbach's conjecture didn't make the Milennium Prize Problems list, and Perleman's refusal of the award for his

I'd say the Riemann hypothesis is more famous. Goldbach's conjecture didn't make the Milennium Prize Problems list, and Perleman's refusal of the award for his proof of the Poincaré conjecture popularized that list quite widely.