Odd numbers as a sum of 3 primes

Prove that if every even natural number greater than 2 is a sum of two prime numbers ( Goldbach conjucture), then every odd number greater than 5 is a sum of three prime numbers.

Proof:

1. Let every number in the Set of Natural numbers greater than 2 be ‘m’
2. m = 2 + 2n [ 2n => Even number]

3. But based on the Goldbach conjucture, m is a sum of 2 primes.
Let p and q be the two primes

m = (2 + 2n) = p + q

4. Let O be the odd number greater than 5
O = m + 3
Note : Since m is greater than 2, so O > 5

5. But m is a sum of 2 primes, so O can be expressed as a sum of 2 primes + 3.
Also, 3 is a prime!

O = p + q + 3

O is expressed as sum of 3 primes.

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useful links

1.Async FIFO design Technique

Async Pointers : Simulation and Synthesis Techniques for Asynchronous FIFO Design

Sync Pointers : Simulation and Synthesis Techniques for Asynchronous FIFO Design
with Asynchronous Pointer Comparisons

2. CDC design and Verification : http://www.sunburst-design.com/papers/CummingsSNUG2008Boston_CDC.pdf

3. Sync and Async Resets : Asynchronous & Synchronous Reset
Design Techniques – Part Deux

 

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8b10b encoding

http://www.latticesemi.com/lit/docs/refdesigns/rd1012.pdf

 

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Typical IP deliverables

  • Hard Macro in Foundary [TSMC/UMC]  node [40nm/65nm] Process [GP/LP process] node
  • GDSII Layout database
  • LVS Net
    • Hard Macro in Foundary [TSMC] 65nm LP process node
    • GDSII Layout database
    • LVS Netlist (cdl) and LVS/DRC verification reports
    • LEF View with physical and pin information
    • Liberty (.lib) view
    • Verilog model
    • RTL files (encrypted)
    • Complete user manual with layout and  integration guidelines
    • Characterization report
    • Datasheet
    • Customer support
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USB2.0 Vs USB3.0

High speed data is clocked at 480.00Mb/s with a data signalling tolerance of ± 500ppm.
Full speed data is clocked at 12.000Mb/s with a data signalling tolerance of ±0.25% or 2,500ppm.
Low speed data is clocked at 1.50Mb/s with a data signalling tolerance of ±1.5% or 15,000ppm.

http://www.beyondlogic.org/usbnutshell/usb2.shtml

§Device Signaling (ERDY) support rather than host polling (PING) as in USB2.0
§Data is not broadcast as in USB2.0 to save power, routing-string information in a packet enables only required hubs/ports between a host and a device

Fast U1 and U2 low power states in addition to traditional suspend (U3)

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LTSSM operation

Detect.idle -> Detect.Active -> Polling.Active – > Polling.Configuration  -> Configuration – > Lane.num -> Lane.Width -> Config.complete -> L0 -> L1 -> L3 – L0

 

 

 

 

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Signal Integrity issues

http://www.allaboutcircuits.com/vol_2/chpt_14/6.html

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