Saint Mary's beacon. [volume] (Leonard Town, Md.) 1867-1983, 1875-09-16

lastly, 4l3 and AS. (we presume. a
Mr.. Baily gives the pairs in this order.
that they were 20 announced by Col
burn The point il Of some importance
In considering the explanation Of the
boys mental procedure). The next feat
was q wonderful one. He was aaked "a
name q number which will divide S..
06S exactly, and he immediately replied
that there il no such number; in 9TH
er words be recognised this number a
what il called Q prime number, or Z
only divisible BY itself and By
unity. just - readily and quickly q
most people would recognize II, 19 o.
23 . such . number. and great deal
naoU quietly thsn probably nine pss.
sons out Of ten would recognize IS OF
50 as such.
Now, il . mathematician were to set
such problem, he would have no 9TH
er resource than to deal with it by di.
rect trial. Of course he would not try
every number from / upward to SO, ,083
He would know that, if the number can
be divided at all, it must be divisible
by q number less than 100; for any
greater divisor would 60, exactly, some
smaller number Of times into Sc, ,OS3
and that smaller aumber would itsell
be a divisor. He would see that the
number is not even, and therefore can.
not be divided by 2, 4, 6, or any even
number. The number is not divisible
by 3; for, according to q well-knowu
rule, il it were, the sum Of its digits
would be SO divisible; therefore he
would at once dismiss 8, 9, Is, and al
numbers divisible by 8 not already dis.
missed. So with (for the number
does not end with s.; SO with z, by
trial; IL, Is, II and so on. But he
would have to try many numbers OF
two and three figures by actual divis-
ion before he had completed his proof
that &c. ,083 has no divisors. Probably
(for we must confess we have not tried)
he would require about quarter of an
hour of calculation before he could be
confident that 6,063 is a prime num-
Der. Here however was a child, eight
years old, who, to all appearance, COM
pleted the work Immediately the num-
Der was proposed
The next feat was of the same na-
ture, but very much more difficult; in
deed it taxed the young calculator 8
powers more than any other feat he ac-
Fermat, mathematician
who gave great attention to the theory
Of numbers, had been led, by reasoning
which need not here BE considered. to
the conclusion that, if the number 2 be
into itself 81 times (that is,
raised TO the thirty-seccad power), and
l added, the result will be prime num-
ber. The resulting number is 1894
967, ,297. The celebrated mathemati.
clan Euler succeeded, however, after a
great deal of labor (and, if the truth
must be told, after a great waste of
time), III showing that this number is
by 641. The number was SUBJ
mitted to Zerah Colburn, who was of
course not informed of Euler's prior
dealing with the problem, and, after a
lapse of some weeks, the cbild-calcula-
tor discovered the result which the vet
eran Swiss mathematician had achieved
with much greater labor.
Before proceeding to inquire how Col
burn achieved these wonders, we must
what was learned about his
processes. He was not very commune
cative,-doubtless because the faculty
be possessed was not accompanied by
clearness of ideas in 9TH
sr matters. In fact, We might as rea-
sonably expect to find a child of eight
years competent to explain processes of
however easily effected, as
10 find him able to explain how he
breathed or spoke. One answer which
be made to q mathematician who press
I'd him more than others to describe
his method was clever, though the
was certainly not to be
ridiculed for trying to get the true ex-
PLANTATION of Colburn's seemingly mys-
Ierious powers-"God," said the child,
'put these things into my head, and 1
cannot put them into yours"
Some things, however, he explained
rs far as he could. He did not seem
able to multiply together, at once, two
numbers which both contained many
figures. He would decompose one or
the other into its factors, and work
with these separately. For instance,
being asked to multiply 1895 bv itself,
he treated 1895 as the product Of 293
and Is, first multiplying 293 by itself,
and then multiplying the product twice
by Is. On being asked to multiply
999, ,999 by itself, he treated it in like
as the product of 37,037 aud
q, getting the correct result. In this
ease, probably, a mathematician would
have got the start Of him, by treating
s99, ,999 as million less one, whence,
by well-known rule, its square is a
million millions and one, less two mil
lions or 999, ,99s, 600, ,OOl. ION being
proceeds the account,
'as to the method by which he obtain
ed these results, the boy constantly de-
clared that he did not know how the
came into his mind. In the
act Of multiplying two numbers togeth-
er, and in the raising of powers, it was
evident (alike from the facts Just stated
and from the motion Of his lips) that
some operation was going forward in
his mind: yet that operation could not.
from the READINGS with which the an
swers were furnished, have been at all
allied to the usual modes Of procedure" "
Baily, after discussing the remarka-
BILE feats Of Zerah Colburn, expressed
the opision that they indicate the exis-
tence of properties of numbers. as yet
undiscovered, somewhat analogous to
those on which the system moflogarithms
is based. and IT," says Carpenter
f.,,ns.oe, BAILEY ssas Zar.h sx~ox~ nlla-