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Block #471,733

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 7:05:41 PM · Difficulty 10.4348 · 6,324,253 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fdc66e6aa77d8887d0e2583dcf92a49312ad69e4d5caf1d9da7e07ac450ef719

View on Chainz ↗

Height

#471,733

Difficulty

10.434790

Transactions

Size

654 B

Version

Bits

0a6f4e5e

Nonce

12,827

Timestamp

4/2/2014, 7:05:41 PM

Confirmations

6,324,253

Merkle Root

2932f510af00f0d90d37209f54b39f9a586f593f5f7b5102694cb0fb4e351b14

Transactions (3)

Coinbase43d15d747bdb45…1ef23a9ab2d38d

1 in → 1 out9.2000 XPM110 B

AeKNrjNj…1NEq95Ta

3d7200836b2cbc…bfbd8f75051fc5

1 in → 3 out9.1700 XPM227 B

AHprswVT…7ysvGhPF AeKNrjNj…1NEq95Ta ALrZxq5u…jReX3z9e

b5aa9873f27160…710246fcdf4f03

1 in → 2 out3.5881 XPM226 B

AR1rBjer…duPei5ts AchEfybk…bK1SmpWx

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.

1.825 × 10⁹⁸(99-digit number)

18256121543132367942…44620015071723098780

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

1.825 × 10⁹⁸(99-digit number)

18256121543132367942…44620015071723098779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.825 × 10⁹⁸(99-digit number)

18256121543132367942…44620015071723098781

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

3.651 × 10⁹⁸(99-digit number)

36512243086264735885…89240030143446197559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.651 × 10⁹⁸(99-digit number)

36512243086264735885…89240030143446197561

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

7.302 × 10⁹⁸(99-digit number)

73024486172529471770…78480060286892395119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.302 × 10⁹⁸(99-digit number)

73024486172529471770…78480060286892395121

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

1.460 × 10⁹⁹(100-digit number)

14604897234505894354…56960120573784790239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.460 × 10⁹⁹(100-digit number)

14604897234505894354…56960120573784790241

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

2.920 × 10⁹⁹(100-digit number)

29209794469011788708…13920241147569580479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.920 × 10⁹⁹(100-digit number)

29209794469011788708…13920241147569580481

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 471733

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 fdc66e6aa77d8887d0e2583dcf92a49312ad69e4d5caf1d9da7e07ac450ef719

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 #471,733 on Chainz ↗