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Block #394,416

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/7/2014, 10:17:26 PM · Difficulty 10.4256 · 6,447,614 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0becbd7fae59ffe4240515253238ebea5877e902dea14071dc3383ce91e6d0d2

View on Chainz ↗

Height

#394,416

Difficulty

10.425564

Transactions

Size

902 B

Version

Bits

0a6cf1cb

Nonce

11,679

Timestamp

2/7/2014, 10:17:26 PM

Confirmations

6,447,614

Merkle Root

977a24bb9338a558d61121a28e2169f112d7362ead4b44417d1b9c1bf0ab7b20

Transactions (1)

Coinbase977a24bb9338a5…1b9c1bf0ab7b20

1 in → 22 out9.1900 XPM811 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn 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.

8.103 × 10⁹⁵(96-digit number)

81037587567252834428…11153399485236989760

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

8.103 × 10⁹⁵(96-digit number)

81037587567252834428…11153399485236989759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.103 × 10⁹⁵(96-digit number)

81037587567252834428…11153399485236989761

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

1.620 × 10⁹⁶(97-digit number)

16207517513450566885…22306798970473979519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.620 × 10⁹⁶(97-digit number)

16207517513450566885…22306798970473979521

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

3.241 × 10⁹⁶(97-digit number)

32415035026901133771…44613597940947959039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.241 × 10⁹⁶(97-digit number)

32415035026901133771…44613597940947959041

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

6.483 × 10⁹⁶(97-digit number)

64830070053802267542…89227195881895918079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.483 × 10⁹⁶(97-digit number)

64830070053802267542…89227195881895918081

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

1.296 × 10⁹⁷(98-digit number)

12966014010760453508…78454391763791836159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.296 × 10⁹⁷(98-digit number)

12966014010760453508…78454391763791836161

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 394416

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 0becbd7fae59ffe4240515253238ebea5877e902dea14071dc3383ce91e6d0d2

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 #394,416 on Chainz ↗

Block #394,416

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