Home/Chain Registry/Block #471,636

Block #471,636

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 5:29:22 PM · Difficulty 10.4349 · 6,340,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13670352cdd36ef2605ca6385f8f49fc51bd2871833bd5e488487649dbfc5d41

View on Chainz ↗

Height

#471,636

Difficulty

10.434870

Transactions

Size

209 B

Version

Bits

0a6f539c

Nonce

126,698

Timestamp

4/2/2014, 5:29:22 PM

Confirmations

6,340,385

Merkle Root

89d1112d36a712785144a3ce32d84aa3805f0a824de114bf69a13f6cf4be4714

Transactions (1)

Coinbase89d1112d36a712…a13f6cf4be4714

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

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.

5.180 × 10¹⁰¹(102-digit number)

51801862266218990845…09715738806851401600

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

5.180 × 10¹⁰¹(102-digit number)

51801862266218990845…09715738806851401599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.180 × 10¹⁰¹(102-digit number)

51801862266218990845…09715738806851401601

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

1.036 × 10¹⁰²(103-digit number)

10360372453243798169…19431477613702803199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.036 × 10¹⁰²(103-digit number)

10360372453243798169…19431477613702803201

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

2.072 × 10¹⁰²(103-digit number)

20720744906487596338…38862955227405606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.072 × 10¹⁰²(103-digit number)

20720744906487596338…38862955227405606401

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

4.144 × 10¹⁰²(103-digit number)

41441489812975192676…77725910454811212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.144 × 10¹⁰²(103-digit number)

41441489812975192676…77725910454811212801

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

8.288 × 10¹⁰²(103-digit number)

82882979625950385352…55451820909622425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.288 × 10¹⁰²(103-digit number)

82882979625950385352…55451820909622425601

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 471636

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 13670352cdd36ef2605ca6385f8f49fc51bd2871833bd5e488487649dbfc5d41

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 #471,636 on Chainz ↗

Block #471,636

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