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Block #451,794

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 4:53:50 AM · Difficulty 10.3799 · 6,341,812 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3075c9bd994d54c31738162fe9ac8288ad5f54cef2c17b63cd4e07dbeeb1b794

View on Chainz ↗

Height

#451,794

Difficulty

10.379900

Transactions

Size

392 B

Version

Bits

0a614119

Nonce

41,409

Timestamp

3/20/2014, 4:53:50 AM

Confirmations

6,341,812

Merkle Root

be83bcec55e92e72c9cbb03e8d296269d72037bfa187a48c739203983ff57e26

Transactions (1)

Coinbasebe83bcec55e92e…9203983ff57e26

1 in → 7 out9.2700 XPM301 B

AHQyfiZn…sQbeqE98 ANKzHTAZ…nyUjaxVT AWCjgrw2…MnFAU7HX AXDyRw5b…CSGugJcJ AUeGuXZm…G5Ehsnka

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.

4.354 × 10⁹⁶(97-digit number)

43543179134531194536…89448421502295336000

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

4.354 × 10⁹⁶(97-digit number)

43543179134531194536…89448421502295335999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.354 × 10⁹⁶(97-digit number)

43543179134531194536…89448421502295336001

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

8.708 × 10⁹⁶(97-digit number)

87086358269062389073…78896843004590671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.708 × 10⁹⁶(97-digit number)

87086358269062389073…78896843004590672001

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

1.741 × 10⁹⁷(98-digit number)

17417271653812477814…57793686009181343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.741 × 10⁹⁷(98-digit number)

17417271653812477814…57793686009181344001

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

3.483 × 10⁹⁷(98-digit number)

34834543307624955629…15587372018362687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.483 × 10⁹⁷(98-digit number)

34834543307624955629…15587372018362688001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.966 × 10⁹⁷(98-digit number)

69669086615249911258…31174744036725375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.966 × 10⁹⁷(98-digit number)

69669086615249911258…31174744036725376001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 451794

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 3075c9bd994d54c31738162fe9ac8288ad5f54cef2c17b63cd4e07dbeeb1b794

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 #451,794 on Chainz ↗