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Block #294,659

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 12:02:15 AM · Difficulty 9.9911 · 6,547,661 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b464636d4f960bdeda6b2c189d84fa18d2e0b7818145db39ce27f64465c40062

View on Chainz ↗

Height

#294,659

Difficulty

9.991123

Transactions

Size

969 B

Version

Bits

09fdba3a

Nonce

99,667

Timestamp

12/5/2013, 12:02:15 AM

Confirmations

6,547,661

Merkle Root

6bf9f36b24c6ec690e67c15d4b5dfae9b76a9f24f11e5e33cdf9865a1d3e12ad

Transactions (1)

Coinbase6bf9f36b24c6ec…f9865a1d3e12ad

1 in → 24 out10.0000 XPM879 B

AcV2etJ3…AC6C3Zed ATiP2myP…qVUH8Grb AWA5FEzr…x9RdPKTy Ad9pSzHt…cpJ3y2zz AVzfxgRz…xjF9JZFi

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.

2.088 × 10⁹⁴(95-digit number)

20889239304224714833…09594950966475295200

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

2.088 × 10⁹⁴(95-digit number)

20889239304224714833…09594950966475295199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.088 × 10⁹⁴(95-digit number)

20889239304224714833…09594950966475295201

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

4.177 × 10⁹⁴(95-digit number)

41778478608449429666…19189901932950590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.177 × 10⁹⁴(95-digit number)

41778478608449429666…19189901932950590401

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

8.355 × 10⁹⁴(95-digit number)

83556957216898859333…38379803865901180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.355 × 10⁹⁴(95-digit number)

83556957216898859333…38379803865901180801

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

1.671 × 10⁹⁵(96-digit number)

16711391443379771866…76759607731802361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.671 × 10⁹⁵(96-digit number)

16711391443379771866…76759607731802361601

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

3.342 × 10⁹⁵(96-digit number)

33422782886759543733…53519215463604723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.342 × 10⁹⁵(96-digit number)

33422782886759543733…53519215463604723201

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 294659

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 b464636d4f960bdeda6b2c189d84fa18d2e0b7818145db39ce27f64465c40062

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 #294,659 on Chainz ↗

Block #294,659

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