Home/Chain Registry/Block #66,412

Block #66,412

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 5:18:37 PM · Difficulty 8.9861 · 6,723,638 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eaa5c4fec71c17dd9f6db6cbc916be7f1300254483b814c61b63365d8ef40ed4

View on Chainz ↗

Height

#66,412

Difficulty

8.986135

Transactions

Size

200 B

Version

Bits

08fc7350

Nonce

800

Timestamp

7/19/2013, 5:18:37 PM

Confirmations

6,723,638

Merkle Root

292d709fbdda1e2ae856e4ec2bc15279e3a24054778fb6e130a130d1657d105e

Transactions (1)

Coinbase292d709fbdda1e…a130d1657d105e

1 in → 1 out12.3700 XPM110 B

Aex6Ue2d…NmvAPnKJ

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.

1.734 × 10⁹⁵(96-digit number)

17348291061486731075…31353096698865862320

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

1.734 × 10⁹⁵(96-digit number)

17348291061486731075…31353096698865862319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.734 × 10⁹⁵(96-digit number)

17348291061486731075…31353096698865862321

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

3.469 × 10⁹⁵(96-digit number)

34696582122973462151…62706193397731724639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.469 × 10⁹⁵(96-digit number)

34696582122973462151…62706193397731724641

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

6.939 × 10⁹⁵(96-digit number)

69393164245946924303…25412386795463449279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.939 × 10⁹⁵(96-digit number)

69393164245946924303…25412386795463449281

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

1.387 × 10⁹⁶(97-digit number)

13878632849189384860…50824773590926898559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.387 × 10⁹⁶(97-digit number)

13878632849189384860…50824773590926898561

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

2.775 × 10⁹⁶(97-digit number)

27757265698378769721…01649547181853797119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 66412

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 eaa5c4fec71c17dd9f6db6cbc916be7f1300254483b814c61b63365d8ef40ed4

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 #66,412 on Chainz ↗