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Block #366,537

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2014, 11:24:19 AM · Difficulty 10.4327 · 6,460,077 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8445d1dbe51f99f5bdda3009056d51d31fcdd851f0a6c6dff8f841afa8b2a73a

View on Chainz ↗

Height

#366,537

Difficulty

10.432683

Transactions

Size

970 B

Version

Bits

0a6ec44b

Nonce

71,657

Timestamp

1/19/2014, 11:24:19 AM

Confirmations

6,460,077

Merkle Root

1ecd27ceb764c699c5453b57cbf21a93132b861d092f8507e6507e6c5562a1ec

Transactions (1)

Coinbase1ecd27ceb764c6…507e6c5562a1ec

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ Ac5JXwCr…tf5C9dQa Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AZV4TwxQ…8JnQqSoH

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.

6.332 × 10⁹⁷(98-digit number)

63321896979392155644…78723537406676372500

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

6.332 × 10⁹⁷(98-digit number)

63321896979392155644…78723537406676372499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.332 × 10⁹⁷(98-digit number)

63321896979392155644…78723537406676372501

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

1.266 × 10⁹⁸(99-digit number)

12664379395878431128…57447074813352744999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.266 × 10⁹⁸(99-digit number)

12664379395878431128…57447074813352745001

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

2.532 × 10⁹⁸(99-digit number)

25328758791756862257…14894149626705489999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.532 × 10⁹⁸(99-digit number)

25328758791756862257…14894149626705490001

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

5.065 × 10⁹⁸(99-digit number)

50657517583513724515…29788299253410979999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.065 × 10⁹⁸(99-digit number)

50657517583513724515…29788299253410980001

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

1.013 × 10⁹⁹(100-digit number)

10131503516702744903…59576598506821959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.013 × 10⁹⁹(100-digit number)

10131503516702744903…59576598506821960001

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 366537

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 8445d1dbe51f99f5bdda3009056d51d31fcdd851f0a6c6dff8f841afa8b2a73a

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 #366,537 on Chainz ↗

Block #366,537

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