Home/Chain Registry/Block #457,595

Block #457,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 12:25:07 AM · Difficulty 10.4207 · 6,343,100 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f629bfb0cb55d685e2efec4dc232999d6a79440ca1943494798afbf3a7d13fde

View on Chainz ↗

Height

#457,595

Difficulty

10.420688

Transactions

Size

1004 B

Version

Bits

0a6bb231

Nonce

758,933

Timestamp

3/24/2014, 12:25:07 AM

Confirmations

6,343,100

Merkle Root

5c22783623d6bd2c80415508f172a11e2aff7dd7ce54fb64f0534bb0588f7297

Transactions (1)

Coinbase5c22783623d6bd…534bb0588f7297

1 in → 25 out9.1900 XPM913 B

AFutDVqJ…TJTJj6UF ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

2.796 × 10⁹⁷(98-digit number)

27962698149508152185…40473215475107603200

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

2.796 × 10⁹⁷(98-digit number)

27962698149508152185…40473215475107603199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.796 × 10⁹⁷(98-digit number)

27962698149508152185…40473215475107603201

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

5.592 × 10⁹⁷(98-digit number)

55925396299016304370…80946430950215206399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.592 × 10⁹⁷(98-digit number)

55925396299016304370…80946430950215206401

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

1.118 × 10⁹⁸(99-digit number)

11185079259803260874…61892861900430412799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.118 × 10⁹⁸(99-digit number)

11185079259803260874…61892861900430412801

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

2.237 × 10⁹⁸(99-digit number)

22370158519606521748…23785723800860825599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.237 × 10⁹⁸(99-digit number)

22370158519606521748…23785723800860825601

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

4.474 × 10⁹⁸(99-digit number)

44740317039213043496…47571447601721651199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.474 × 10⁹⁸(99-digit number)

44740317039213043496…47571447601721651201

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 457595

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 f629bfb0cb55d685e2efec4dc232999d6a79440ca1943494798afbf3a7d13fde

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 #457,595 on Chainz ↗