Home/Chain Registry/Block #654,124

Block #654,124

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/30/2014, 12:05:55 AM · Difficulty 10.9552 · 6,137,578 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ad6915ff519834853ea69a1562987de38473ff3e959f821bd05539ee260b981

View on Chainz ↗

Height

#654,124

Difficulty

10.955187

Transactions

Size

120.30 KB

Version

Bits

0af4872a

Nonce

61,367,069

Timestamp

7/30/2014, 12:05:55 AM

Confirmations

6,137,578

Merkle Root

d7ca24ef53205b54211a4017ae61b163ae8d29c330198c6348bdd9e3caddca08

Transactions (3)

Coinbasec6594d836ac95f…c2fbea3dd889f2

1 in → 1 out9.5600 XPM116 B

ANSXnLY2…Sd25TjkD

f1a52a0da37241…bb9c44d544a9d4

409 in → 2 out500.0100 XPM59.17 KB

AUE5QneS…bDZqwQ1J AcTpMBRy…JbS2tRao

5c5a0885fc65ed…4dfabd5e527d7a

421 in → 2 out500.0100 XPM60.93 KB

AN3qpHzd…Y3HvvxaY AUE5QneS…bDZqwQ1J

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.

5.853 × 10⁹⁵(96-digit number)

58534821795065803591…77661240838259131920

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

5.853 × 10⁹⁵(96-digit number)

58534821795065803591…77661240838259131919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.853 × 10⁹⁵(96-digit number)

58534821795065803591…77661240838259131921

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

1.170 × 10⁹⁶(97-digit number)

11706964359013160718…55322481676518263839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.170 × 10⁹⁶(97-digit number)

11706964359013160718…55322481676518263841

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

2.341 × 10⁹⁶(97-digit number)

23413928718026321436…10644963353036527679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.341 × 10⁹⁶(97-digit number)

23413928718026321436…10644963353036527681

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

4.682 × 10⁹⁶(97-digit number)

46827857436052642873…21289926706073055359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.682 × 10⁹⁶(97-digit number)

46827857436052642873…21289926706073055361

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

9.365 × 10⁹⁶(97-digit number)

93655714872105285746…42579853412146110719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.365 × 10⁹⁶(97-digit number)

93655714872105285746…42579853412146110721

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

1.873 × 10⁹⁷(98-digit number)

18731142974421057149…85159706824292221439

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 654124

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 0ad6915ff519834853ea69a1562987de38473ff3e959f821bd05539ee260b981

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 #654,124 on Chainz ↗