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Block #461,447

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 5:48:27 PM · Difficulty 10.4152 · 6,369,674 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5de7bbef8dac60c57174e53670a0d0e65c96da322a7365aab3def9530ad62021

View on Chainz ↗

Height

#461,447

Difficulty

10.415211

Transactions

Size

1.31 KB

Version

Bits

0a6a4b3e

Nonce

11,894

Timestamp

3/26/2014, 5:48:27 PM

Confirmations

6,369,674

Merkle Root

8657ad279b3a82ad05349fb95b67942603387e7edc0262896e7ce36ef2bc332f

Transactions (3)

Coinbasefb5f130c383cc7…710a4a9ef831ce

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

543225efd5986d…84582d8320ea53

5 in → 2 out10.0100 XPM819 B

AGhK9uxx…eMYnZfLE AQuAFktq…QSLjh5cK

7dc4b8a0fa4270…32fe1e5a57dba0

2 in → 2 out18.4900 XPM307 B

AdmjimzU…zLXfXgqZ AeHGPekq…SMwoaN7L

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.

3.211 × 10¹⁰⁵(106-digit number)

32117196860386733550…62525005619894681600

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

3.211 × 10¹⁰⁵(106-digit number)

32117196860386733550…62525005619894681599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.211 × 10¹⁰⁵(106-digit number)

32117196860386733550…62525005619894681601

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

6.423 × 10¹⁰⁵(106-digit number)

64234393720773467100…25050011239789363199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.423 × 10¹⁰⁵(106-digit number)

64234393720773467100…25050011239789363201

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

1.284 × 10¹⁰⁶(107-digit number)

12846878744154693420…50100022479578726399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.284 × 10¹⁰⁶(107-digit number)

12846878744154693420…50100022479578726401

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

2.569 × 10¹⁰⁶(107-digit number)

25693757488309386840…00200044959157452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.569 × 10¹⁰⁶(107-digit number)

25693757488309386840…00200044959157452801

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

5.138 × 10¹⁰⁶(107-digit number)

51387514976618773680…00400089918314905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.138 × 10¹⁰⁶(107-digit number)

51387514976618773680…00400089918314905601

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 461447

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 5de7bbef8dac60c57174e53670a0d0e65c96da322a7365aab3def9530ad62021

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 #461,447 on Chainz ↗

Block #461,447

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