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Block #1,406,673

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2016, 1:37:53 AM · Difficulty 10.8067 · 5,436,295 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9609f9ff775ed8f3bcd9714a6b569a96949a80604719080cc79f7690fa10f297

View on Chainz ↗

Height

#1,406,673

Difficulty

10.806659

Transactions

Size

425 B

Version

Bits

0ace812c

Nonce

88,240,259

Timestamp

1/10/2016, 1:37:53 AM

Confirmations

5,436,295

Merkle Root

ef20859d3fbc5a1dcf4ac777cc9fe80cb55d6160cae0fc14591654a279e7ae77

Transactions (2)

Coinbase27f7249d8c453c…47f48db7dd9f60

1 in → 1 out8.5600 XPM110 B

ARhmZtzm…XNuLCZE7

498efd3564ef36…11acf034dfcb51

1 in → 2 out159304.5827 XPM225 B

AQz5cxT1…6bpmEdXY ASdeM36j…S1zDiYpo

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.

1.788 × 10⁹⁵(96-digit number)

17881870146724838958…05373319675155694720

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

1.788 × 10⁹⁵(96-digit number)

17881870146724838958…05373319675155694719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.788 × 10⁹⁵(96-digit number)

17881870146724838958…05373319675155694721

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

3.576 × 10⁹⁵(96-digit number)

35763740293449677916…10746639350311389439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.576 × 10⁹⁵(96-digit number)

35763740293449677916…10746639350311389441

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

7.152 × 10⁹⁵(96-digit number)

71527480586899355833…21493278700622778879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.152 × 10⁹⁵(96-digit number)

71527480586899355833…21493278700622778881

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

1.430 × 10⁹⁶(97-digit number)

14305496117379871166…42986557401245557759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.430 × 10⁹⁶(97-digit number)

14305496117379871166…42986557401245557761

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

2.861 × 10⁹⁶(97-digit number)

28610992234759742333…85973114802491115519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.861 × 10⁹⁶(97-digit number)

28610992234759742333…85973114802491115521

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 1406673

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 9609f9ff775ed8f3bcd9714a6b569a96949a80604719080cc79f7690fa10f297

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 #1,406,673 on Chainz ↗

Block #1,406,673

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