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What a fascinating question !

I examined the first 43,000 prime numbers ... up to 519,287 .

The first pair of primes that differ by at least 100 is 370,261 and 370,373.

They are the 31,546th and 31,547th primes, and the difference is 112.

The only other pairs in the first 43,000 primes with differences of 100 or more are:

33,609th and 33,610th primes: 396,733 and 396,833, difference = 100

40,934th and 40935th primes: 492,113 and 492,227, difference = 114

Interesting how the difference of 112 occurs before the difference of 100.

(It's completely tasteless, frowned upon, and forbidden for a person like me

who writes an answer he's proud of to then shamelessly ask for a Trust Point.)

The first 10 pairs of consecutive primes that differ by at least 100 are:

(370261, 370373), (396733, 396833), (492113, 492227), (838249, 838349), (1098847, 1098953), (1313467, 1313567), (1349533, 1349651), (1357201, 1357333), (1388483, 1388587), (1444309, 1444411)

The first 10 pairs of consecutive primes that differ by exactly 100 are:

(396733, 396833), (838249, 838349), (1313467, 1313567), (1648081, 1648181), (1655707, 1655807), (2345989, 2346089), (2784373, 2784473), (3254959, 3255059), (3595489, 3595589), (4047157, 4047257)

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Q: What are two consecutive prime numbers whose difference is at least 100?
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