Photons generated by nuclear fusion in the sun's core take approximately 17,000 to 100,000 years to diffuse through the radiative zone to the surface.
"the hydrogen fusion, whatever, that happens in the sun's core, that release that releases gamma rays, which if they went through, they'll just like literally sever your DNA... They bounce around in the sun's core. That original light that's, you know, originated in that reaction bounces around the core for like 17,000 to 100,000 years in the core, then it gets to the surface and shoots out in like 8 seconds if that." (said at 2:36:08)
No published record matching the claim that photons diffuse from the sun's core to the surface in approximately 17,000 to 100,000 years was located; this does not prove the claim false.
corroborated by web sources
Astrophysical models and scientific sources confirm that energy generated by nuclear fusion in the Sun's core takes tens of thousands to over 100,000 years (commonly cited between 10,000 and 170,000 years) to diffuse through the solar interior to the surface. This delay is caused by the dense plasma repeatedly scattering, absorbing, and re-emitting photons in a process known as a random walk.