Home/Chain Registry/Block #551,710

Block #551,710

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/19/2014, 12:08:24 AM · Difficulty 10.9624 · 6,248,962 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40903de74f7814106fdb7e12e2b58144824ec40df72e373cd0376a191b8ef25a

View on Chainz ↗

Height

#551,710

Difficulty

10.962431

Transactions

Size

764 B

Version

Bits

0af661db

Nonce

58,126

Timestamp

5/19/2014, 12:08:24 AM

Confirmations

6,248,962

Merkle Root

1b51595e675b6bd344010fc1d101a636835e0901285343ab6355d8bfc80f7e56

Transactions (1)

Coinbase1b51595e675b6b…55d8bfc80f7e56

1 in → 18 out8.3100 XPM675 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 AJzWx2VD…j4ZSMit5 AdxPNkWD…ZMa9u34q AJtNW28X…Syb4Ph5j

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.

1.822 × 10⁹²(93-digit number)

18224276058826047665…00444920444350720000

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

1.822 × 10⁹²(93-digit number)

18224276058826047665…00444920444350719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.822 × 10⁹²(93-digit number)

18224276058826047665…00444920444350720001

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

3.644 × 10⁹²(93-digit number)

36448552117652095331…00889840888701439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.644 × 10⁹²(93-digit number)

36448552117652095331…00889840888701440001

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

7.289 × 10⁹²(93-digit number)

72897104235304190663…01779681777402879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.289 × 10⁹²(93-digit number)

72897104235304190663…01779681777402880001

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

1.457 × 10⁹³(94-digit number)

14579420847060838132…03559363554805759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.457 × 10⁹³(94-digit number)

14579420847060838132…03559363554805760001

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

2.915 × 10⁹³(94-digit number)

29158841694121676265…07118727109611519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.915 × 10⁹³(94-digit number)

29158841694121676265…07118727109611520001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.831 × 10⁹³(94-digit number)

58317683388243352530…14237454219223039999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 551710

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 40903de74f7814106fdb7e12e2b58144824ec40df72e373cd0376a191b8ef25a

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 #551,710 on Chainz ↗