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Block #379,866

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 7:55:18 PM · Difficulty 10.4196 · 6,445,098 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd096760d716974f2cce9327946d3c1f8aee4f11aabb9fe5e0c1927e8d96b6d9

View on Chainz ↗

Height

#379,866

Difficulty

10.419645

Transactions

Size

970 B

Version

Bits

0a6b6dd6

Nonce

277,570

Timestamp

1/28/2014, 7:55:18 PM

Confirmations

6,445,098

Merkle Root

655676c36591b46bdaf2143f421e4a3643d1ace4f7f02c0831c49eacc1d2830d

Transactions (1)

Coinbase655676c36591b4…c49eacc1d2830d

1 in → 24 out9.2000 XPM879 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AKzkYQaQ…zR4FspJZ

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.

2.828 × 10⁹⁷(98-digit number)

28280408717394947783…79688282836454044240

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

2.828 × 10⁹⁷(98-digit number)

28280408717394947783…79688282836454044239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.828 × 10⁹⁷(98-digit number)

28280408717394947783…79688282836454044241

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

5.656 × 10⁹⁷(98-digit number)

56560817434789895566…59376565672908088479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.656 × 10⁹⁷(98-digit number)

56560817434789895566…59376565672908088481

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

1.131 × 10⁹⁸(99-digit number)

11312163486957979113…18753131345816176959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.131 × 10⁹⁸(99-digit number)

11312163486957979113…18753131345816176961

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

2.262 × 10⁹⁸(99-digit number)

22624326973915958226…37506262691632353919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.262 × 10⁹⁸(99-digit number)

22624326973915958226…37506262691632353921

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

4.524 × 10⁹⁸(99-digit number)

45248653947831916453…75012525383264707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.524 × 10⁹⁸(99-digit number)

45248653947831916453…75012525383264707841

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 379866

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 cd096760d716974f2cce9327946d3c1f8aee4f11aabb9fe5e0c1927e8d96b6d9

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 #379,866 on Chainz ↗

Block #379,866

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