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Block #330,924

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 12:26:24 AM · Difficulty 10.1687 · 6,495,990 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ced85ac6f20e08ca0b7325bd77211ff91801d46c1c55bbf582867c7c0844e23c

View on Chainz ↗

Height

#330,924

Difficulty

10.168738

Transactions

Size

657 B

Version

Bits

0a2b3265

Nonce

161,334

Timestamp

12/27/2013, 12:26:24 AM

Confirmations

6,495,990

Merkle Root

212f1bb25e39788aad35b12ac0de8790d730f88025f4e60be344722a1b2db052

Transactions (3)

Coinbase7c39ca8d38f375…5afb96dbe75ecf

1 in → 1 out9.6800 XPM110 B

AeKNrjNj…1NEq95Ta

4b21a9b0123bc5…f9c0d1e21b3121

1 in → 2 out5.4122 XPM227 B

AXy8CJrT…rHLoyh3A AbWyQfaZ…byEU7Zob

5199df08570400…e4525f244de5e7

1 in → 2 out2.3072 XPM227 B

ANYyZm6t…sENep948 AdMzUrLG…ewJSjLyd

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.

1.507 × 10¹⁰²(103-digit number)

15077145337598721481…15907261779384806400

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

1.507 × 10¹⁰²(103-digit number)

15077145337598721481…15907261779384806399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.507 × 10¹⁰²(103-digit number)

15077145337598721481…15907261779384806401

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

3.015 × 10¹⁰²(103-digit number)

30154290675197442962…31814523558769612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.015 × 10¹⁰²(103-digit number)

30154290675197442962…31814523558769612801

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

6.030 × 10¹⁰²(103-digit number)

60308581350394885925…63629047117539225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.030 × 10¹⁰²(103-digit number)

60308581350394885925…63629047117539225601

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

1.206 × 10¹⁰³(104-digit number)

12061716270078977185…27258094235078451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.206 × 10¹⁰³(104-digit number)

12061716270078977185…27258094235078451201

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

2.412 × 10¹⁰³(104-digit number)

24123432540157954370…54516188470156902399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.412 × 10¹⁰³(104-digit number)

24123432540157954370…54516188470156902401

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 330924

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 ced85ac6f20e08ca0b7325bd77211ff91801d46c1c55bbf582867c7c0844e23c

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 #330,924 on Chainz ↗

Block #330,924

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