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Block #249,759

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 3:37:09 AM · Difficulty 9.9673 · 6,575,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48dbb8ddb5478de1e84ab9c2214a7f7b3fe296d12e08d646bbdacdb82e63a20e

View on Chainz ↗

Height

#249,759

Difficulty

9.967287

Transactions

Size

1.78 KB

Version

Bits

09f7a021

Nonce

8,186

Timestamp

11/8/2013, 3:37:09 AM

Confirmations

6,575,738

Merkle Root

5099ee35fc6455e659c6e3a59d8373418f6d03bd840e02b1031113dea4de765e

Transactions (1)

Coinbase5099ee35fc6455…1113dea4de765e

1 in → 49 out10.0300 XPM1.69 KB

ARskhKeb…UgDvvX9P AdnG9gQ7…N9B7mA2p ALvvKn4M…Sj4tF2ge ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

2.545 × 10⁹⁷(98-digit number)

25450223920303169286…27421062835782095360

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

2.545 × 10⁹⁷(98-digit number)

25450223920303169286…27421062835782095359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.545 × 10⁹⁷(98-digit number)

25450223920303169286…27421062835782095361

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

5.090 × 10⁹⁷(98-digit number)

50900447840606338573…54842125671564190719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.090 × 10⁹⁷(98-digit number)

50900447840606338573…54842125671564190721

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

1.018 × 10⁹⁸(99-digit number)

10180089568121267714…09684251343128381439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.018 × 10⁹⁸(99-digit number)

10180089568121267714…09684251343128381441

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

2.036 × 10⁹⁸(99-digit number)

20360179136242535429…19368502686256762879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.036 × 10⁹⁸(99-digit number)

20360179136242535429…19368502686256762881

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

4.072 × 10⁹⁸(99-digit number)

40720358272485070858…38737005372513525759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.072 × 10⁹⁸(99-digit number)

40720358272485070858…38737005372513525761

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 249759

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 48dbb8ddb5478de1e84ab9c2214a7f7b3fe296d12e08d646bbdacdb82e63a20e

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 #249,759 on Chainz ↗

Block #249,759

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