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I've heard about year 2038 problem and I'm worried I've read about Bitcoin measuring time with 32 bits, why aren't developers worried about Y2038P only 15 years away?

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Y2038P was about signed integers.

In Bitcoin, block time is an unsigned integer, such case doesn't correspond to a Y2038P, but a Y2107P.

Thus the numbers are loosely these:

2^32 / 60 / 60 / 24 / 365.25 ~= 136;
1970 + 136 = 2106

instead of these:

2^32 / 60 / 60 / 24 / 365.25 / 2 ~= 68;
1970 + 68 = 2038

Because we will be dead by 2106, it's not current developers task to worry about.

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