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Euler ascertained that 2 31 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 2 30 (2 31 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they ...
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The Class P1 was a freight derivative of his famed Class A1 4-6-2, inspired by the Pennsylvania Railroad's twin K4s 4-6-2 and L1s 2-8-2 locomotives. Two were built, but there was never really much call for their ability and they remained under-utilised throughout their short existence.
The release on December 8, 1998 and subsequent releases through J2SE 5.0 were rebranded retrospectively Java 2 and the version name "J2SE" (Java 2 Platform, Standard Edition) replaced JDK to distinguish the base platform from J2EE (Java 2 Platform, Enterprise Edition) and J2ME (Java 2 Platform, Micro Edition). This was a very significant ...
The only known powers of 2 with all digits even are 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^6 = 64 and 2^11 = 2048. [11] The first 3 powers of 2 with all but last digit odd is 2^4 = 16, 2^5 = 32 and 2^9 = 512. The next such power of 2 of form 2^n should have n of at least 6 digits.
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
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According to the Erdős–Szekeres theorem, any sequence of + distinct integers has an increasing or a decreasing subsequence of length + [7] [8] For inputs in which each permutation of the input is equally likely, the expected length of the longest increasing subsequence is approximately . [9] [2]