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Block #383,282

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2014, 7:55:56 AM · Difficulty 10.3991 · 6,442,042 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05cb3857fbf234e3cc382d2f7453b9f493ff26a4685a01743a3dc6ca4e940bea

View on Chainz ↗

Height

#383,282

Difficulty

10.399090

Transactions

Size

764 B

Version

Bits

0a662abc

Nonce

105,241

Timestamp

1/31/2014, 7:55:56 AM

Confirmations

6,442,042

Merkle Root

8799d86a0482d6fd8a9aab0d93e5610c090943620d8c73f8c85188676ee69443

Transactions (1)

Coinbase8799d86a0482d6…5188676ee69443

1 in → 18 out9.2300 XPM675 B

AQvZBsUo…hppgRZTJ AXX1wTMN…FfSE8V61 AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 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.

4.518 × 10⁹¹(92-digit number)

45181672619051155409…63914417241050452000

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

4.518 × 10⁹¹(92-digit number)

45181672619051155409…63914417241050451999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.518 × 10⁹¹(92-digit number)

45181672619051155409…63914417241050452001

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

9.036 × 10⁹¹(92-digit number)

90363345238102310819…27828834482100903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.036 × 10⁹¹(92-digit number)

90363345238102310819…27828834482100904001

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

1.807 × 10⁹²(93-digit number)

18072669047620462163…55657668964201807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.807 × 10⁹²(93-digit number)

18072669047620462163…55657668964201808001

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

3.614 × 10⁹²(93-digit number)

36145338095240924327…11315337928403615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.614 × 10⁹²(93-digit number)

36145338095240924327…11315337928403616001

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

7.229 × 10⁹²(93-digit number)

72290676190481848655…22630675856807231999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.229 × 10⁹²(93-digit number)

72290676190481848655…22630675856807232001

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 383282

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 05cb3857fbf234e3cc382d2f7453b9f493ff26a4685a01743a3dc6ca4e940bea

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 #383,282 on Chainz ↗

Block #383,282

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