Home/Chain Registry/Block #42,320

Block #42,320

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 6:23:24 PM · Difficulty 8.5926 · 6,750,698 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

96c6cc81f9efc227b85c7c207e009093a437ce3857c74c69be0a17c4dc9cca75

View on Chainz ↗

Height

#42,320

Difficulty

8.592568

Transactions

Size

204 B

Version

Bits

0897b284

Nonce

1,494

Timestamp

7/14/2013, 6:23:24 PM

Confirmations

6,750,698

Merkle Root

cae23d384cd26c38cf4c907460a84449865db4d8d343277e36566864861dea9f

Transactions (1)

Coinbasecae23d384cd26c…566864861dea9f

1 in → 1 out13.5300 XPM110 B

AXWphP8T…4trwmtBM

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.844 × 10¹⁰⁵(106-digit number)

38440057931521457056…00892685331341303520

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.844 × 10¹⁰⁵(106-digit number)

38440057931521457056…00892685331341303519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.844 × 10¹⁰⁵(106-digit number)

38440057931521457056…00892685331341303521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.688 × 10¹⁰⁵(106-digit number)

76880115863042914113…01785370662682607039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.688 × 10¹⁰⁵(106-digit number)

76880115863042914113…01785370662682607041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.537 × 10¹⁰⁶(107-digit number)

15376023172608582822…03570741325365214079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.537 × 10¹⁰⁶(107-digit number)

15376023172608582822…03570741325365214081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.075 × 10¹⁰⁶(107-digit number)

30752046345217165645…07141482650730428159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.075 × 10¹⁰⁶(107-digit number)

30752046345217165645…07141482650730428161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 8

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 42320

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 96c6cc81f9efc227b85c7c207e009093a437ce3857c74c69be0a17c4dc9cca75

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #42,320 on Chainz ↗