I deduce that Euler was the first person who discovered the smallest irregular
prime number 37 in zeta values around 1735. Kummer was the
first person who discovered it in class numbers of
p-cyclotomic fields around 1850.
Euler's discoveries seem to have been hidden in errors of
the six (or seven) lists of approximated values in
E101("Introduction to the Analysis of the Infinite", volume 1).
Furthermore the error checks seem to have been hidden in the errors
of some values (log pi, cos 1, sin 1 etc.) in E102 (volume 2).
Twenty years after the publishment of E101, he also gave
explicit/implicit answers in E343 "Letters to a German princess"
and E352 "Remarks on a beautiful relationship between series of
powers and reciprocals of powers".
Why did he hide them? It would be very interesting to deliberate the reason.
It is really deep and essential.
The following contents are hints and answers.
(37,32=2^2*8)
(59,44=2^2*11)
(67,58=2^1*(13+16))
(101,68=2^1*(13+21))
(103,24=2^0*24)
the number of total errors=7 irregular primes (37, 59, 67, 101, 103, 131, 149)