The blog post you found cites a very fun journal article, but doesn't discuss it very well, denying the fun to all of us. The origin of this legend was figured out in 2005 and the results are available for all to read.
The most prominent figure we see in these anecdotes was a conscious hoax by peace activist Norman Cousins in 1953; Cousins claimed to newspaper readers that the "Norwegian Academy of Science" discovered only 292 years of peace since 3600 BC, and 14,513 wars since then. These were meant to be absurdly overspecific figures, and the headline in the newspaper in which his article appeared calls his work an "Imaginary Experiment".
But the idea seems to have existed before Cousins's hoax. In particular, a magazine called the Moskovskie Vedomosti claimed that there had been 227 years of peace, and 268 wars (not years of war; this was possibly misremembered by later authors). But the Vedomosti could not be located by the authors of this study, and in any case there seemed to be several figures floating around. The authors ran across a similar claim by a writer named Bloch, and are pleased at their good fortune when they find him:
For it so happens that Bloch, in a tiny note, refers to his source: a
Russian military encyclopedia Encyclopädie der Kriegs- und
Marinewissenschaften (St. Petersburg, 1885). We were lucky enough to
obtain a copy of the article in the encyclopedia Bloch refers to -
after many months of writing to libraries all over the world, to no
In the lemma on war Lieut. General G.A. Leer refers, in his turn, to
his source of the war figures: the work of the French philosopher
Odysse Barot Lettres sur la Philosophie de l'Histoire (Paris, 1864).
We were afraid that this work, too, would refer to another, yet more
ancient, source, and that that source would, in its turn, refer to a
still more ancient one, in a kind of infinite regression. But again we
were lucky enough (after many a month of writing to libraries in
France, to no avail), to obtain a copy, and this time we hit the
jackpot: Barot's book is indubitably the one and only primordial
original Source of sources; totally obscure itself, but immortalized
by the myth it helped to create.
The original text is quoted; it presents the author's count of peace treaties that have been signed, and his tabulation of 227 years of peace, which seems (implicitly) to presume that times before peace treaties are signed are times of war.
But what exactly do these figures mean, presuming of course that Barot
did not dream them up but actually catalogued and counted all these
treaties (which is uncertain as he nowhere presents such a list: we
have to believe him on his word)? As may be gathered from the
quotation above, what Barot actually counted were peace treaties along
with alliance and amity treaties, and NOT WARS. Cousins, as well as
all of his predecessors, have drawn the totally unsubstantiated
conclusion that the number of peace treaties equals the number of
wars, under the assumption that all wars are ended by means of peace
treaties. But apart from the volatility of such an assumption, it is
not only peace treaties Barot counted, but also treaties of alliance
and amity, and these do not necessarily, or not at all, justify the
assumption of warlike activities.
The paywalled article that referenced this essay could find no scientific source for claims of two hundred and XX years of peace, and even the French source cited in this essay does not explain his methodology.