Pete-3.c

pete-3.c is one of the nine entries an anonymous "Pete" submitted to Bignum Bakeoff,http://djm.cc/bignum-results.txt and the smallest entry that produces a large number. It uses the <<, which in the fictional Bignum Bakeoff machine may be defined as \(a \ll b = a \cdot 2^b\) for nonnegative \(a\) and \(b\). (Its behavior is more complex in standard C implementations.)
Presumably to save space, Pete did not use parentheses. Unfortunately, << is left-associative, and \(a \ll b\) grows much faster relative to \(b\) than to \(a\).http://en.cppreference.com/w/c/language/operator_precedence So the returned value becomes \(9 \cdot (2^9)^{163} \cdot 2^{99} \approx 2.33 \cdot 10^{472}\), between a centillion and googolding. A large amount of space is therefore wasted on a number smaller than 1 << 1,600. If the operator was instead right-to-left associative, the output would grow at a roughly tetrational rate with respect to the number of 9's.
The full decimal expansion of this number is:
Its prime factorization is 21,566 × 32.
== Code ==
int main() 
{ 
 return 
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 <<
 9 << 9 << 9 << 9 << 9 << 9 << 9 << 9 << 99; 
}
==Approximations==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(2.329\times10^{472}\) 	\(2.33\times10^{472}\)
Arrow notation 	\(42\uparrow291\) 	\(218\uparrow202\)
Steinhaus-Moser Notation 	204[3] 	205[3]
Copy notation 	2[473] 	3[473]
Taro's multivariable Ackermann function	A(3,1566) 	A(3,1567)
Pound-Star Notation 	#*((4918))*13 	#*((4919))*13
BEAF 	{42,291} 	{218,202}
Hyper-E notation 	E[42]291 	E[218]202
Bashicu matrix system 	(0)(0)(0)(0)(0)(0)(0)[4901] 	(0)(0)(0)(0)(0)(0)(0)[4902]
Hyperfactorial array notation 	241! 	242!
Fast-growing hierarchy 	\(f_2(1558)\) 	\(f_2(1559)\)
Hardy hierarchy 	\(H_{\omega^2}(1558)\) 	\(H_{\omega^2}(1559)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^3+\omega+3}+\omega^{\omega^3+\omega+2}}(8)\)	\(g_{\omega^{\omega^3+\omega+3}+\omega^{\omega^3+\omega+2}}(8)\)
== Sources ==
== See also ==
Category:Numbers
Category:Bignum Bakeoff contestant
Category:Class 2
Category:Computers
Category:Numbers with 101 to 999 digits
Category:Perfect powers