user46112: I read in this atmega328p datasheet the following on page 308:
From sect. 28.4:

By default, the successive approximation circuitry requires an input
clock frequency between 50kHz and 200kHz to get maximum resolution. If
a lower resolution than 10 bits is needed, the input clock frequency
to the ADC can be higher than 200kHz to get a higher sample rate.
The
ADC module contains a prescaler, which generates an acceptable ADC
clock frequency from any CPU frequency above 100kHz. The prescaling is
selected by the ADC Prescaler Select bits in the ADC Control and
Status Register A (ADCSRA.ADPS). The prescaler starts counting from
the moment the ADC is switched on by writing the ADC Enable bit
ADCSRA.ADEN to '1'. The prescaler keeps running for as long as ADEN=1,
and is continuously reset when ADEN=0.
When initiating a single ended
conversion by writing a '1' to the ADC Start Conversion bit
(ADCSRA.ADSC), the conversion starts at the following rising edge of
the ADC clock cycle.
A normal conversion takes 13 ADC clock cycles.
The first conversion after the ADC is switched on (i.e., ADCSRA.ADEN
is written to '1') takes 25 ADC clock cycles in order to initialize
the analog circuitry.

By required bandwidth is 120 kHz, and 5 bit accuracy will suffice for my purpose. So, I understand that I can achieve this by changing the prescaler to a lower division number, thus increasing the clock frequency fed into the ADC (as per the diagram in the aforementioned document).
However, the document only specifies the min and max times required for ADC conversion for 50 kHz (12 to 280 microseconds at 50kHz bandwidth).
My question: Given my requirement of 120kHz bandwidth, what is the lowest prescaler division value I should use to guarantee ADC completion time to within 1/120kHz seconds (8.3us)?
EDIT: This is another question I have: Why does the accuracy change when using a lower divider value? Surely we are simply changing the clock frequency fed into the ADC converter, not the ADC algorithm itself; so why should the bit accuracy change?

user46112: From: http://forum.arduino.cc/index.php?topic=6549.0
The documentation states that 13 cycles are neccesary for ADC conversion. Thus, using the clk/13*8 divisor configuration, and 16 MHz system clock, the upper bound becomes 154KHz
The forum post in the above link continues to say that "ADC clock frequencies above 1MHz are uncharacterised", however this was quoting another document for which the link is dead. I could not find this statement in the most recent documentation.
Edit: Another forum post where a user successfully used an atmega328p to achieve 360000 samples/sec, so it is technically possible:
http://forum.arduino.cc/index.php?topic=8795.0

46112: <p>I read in this <a href="http://ww1.microchip.com/downloads/en/DeviceDoc/Atmel-42735-8-bit-AVR-Microcontroller-ATmega328-328P_Datasheet.pdf" rel="nofollow noreferrer">atmega328p datasheet</a> the following on page 308:</p>
<p>From sect. 28.4:</p>
<blockquote>
<p>By default, the successive approximation circuitry requires an input
clock frequency between 50kHz and 200kHz to get maximum resolution. If
a lower resolution than 10 bits is needed, the input clock frequency
to the ADC can be higher than 200kHz to get a higher sample rate.</p>
<p>The
ADC module contains a prescaler, which generates an acceptable ADC
clock frequency from any CPU frequency above 100kHz. The prescaling is
selected by the ADC Prescaler Select bits in the ADC Control and
Status Register A (ADCSRA.ADPS). The prescaler starts counting from
the moment the ADC is switched on by writing the ADC Enable bit
ADCSRA.ADEN to '1'. The prescaler keeps running for as long as ADEN=1,
and is continuously reset when ADEN=0.</p>
<p>When initiating a single ended
conversion by writing a '1' to the ADC Start Conversion bit
(ADCSRA.ADSC), the conversion starts at the following rising edge of
the ADC clock cycle.</p>
<p>A normal conversion takes 13 ADC clock cycles.
The first conversion after the ADC is switched on (i.e., ADCSRA.ADEN
is written to '1') takes 25 ADC clock cycles in order to initialize
the analog circuitry.</p>
</blockquote>
<p>By required bandwidth is 120 kHz, and 5 bit accuracy will suffice for my purpose. So, I understand that I can achieve this by changing the prescaler to a lower division number, thus increasing the clock frequency fed into the ADC (as per the diagram in the aforementioned document).</p>
<p>However, the document only specifies the min and max times required for ADC conversion for 50 kHz (12 to 280 microseconds at 50kHz bandwidth).</p>
<p>My question: Given my requirement of 120kHz bandwidth, what is the lowest prescaler division value I should use to guarantee ADC completion time to within 1/120kHz seconds (8.3us)?</p>
<p>EDIT: This is another question I have: Why does the accuracy change when using a lower divider value? Surely we are simply changing the clock frequency fed into the ADC converter, not the ADC algorithm itself; so why should the bit accuracy change?</p>
 46112: <p>From: <a href="http://forum.arduino.cc/index.php?topic=6549.0" rel="nofollow noreferrer">http://forum.arduino.cc/index.php?topic=6549.0</a></p>

<p>The documentation states that 13 cycles are neccesary for ADC conversion. Thus, using the clk/13*8 divisor configuration, and 16 MHz system clock, the upper bound becomes 154KHz</p>

<p>The forum post in the above link continues to say that "ADC clock frequencies above 1MHz are uncharacterised", however this was quoting another document for which the link is dead. I could not find this statement in the most recent documentation.</p>

<p>Edit: Another forum post where a user successfully used an atmega328p to achieve 360000 samples/sec, so it is technically possible:
<a href="http://forum.arduino.cc/index.php?topic=8795.0" rel="nofollow noreferrer">http://forum.arduino.cc/index.php?topic=8795.0</a></p>
