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Block #749,441

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/2/2014, 6:04:56 AM · Difficulty 10.9764 · 6,077,542 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

554b051885ffd3201b0401eac116fa20d95b95f098a75c2963775ce8f9548e65

View on Chainz ↗

Height

#749,441

Difficulty

10.976365

Transactions

Size

1023 B

Version

Bits

0af9f30e

Nonce

596,395,998

Timestamp

10/2/2014, 6:04:56 AM

Confirmations

6,077,542

Merkle Root

d16738fc1dc0154a76b44e0a7bbbe5aeda5c5e701f246f5c327b27dd76acd351

Transactions (4)

Coinbase05f8c7ba7c6972…569ca35409f36e

1 in → 1 out8.3200 XPM109 B

AWd1Ms6h…DPZ6ffts

4f2c960083010c…1a7bb2dc8326a9

2 in → 2 out10.8056 XPM372 B

AeSCDTjX…MwtoboZd AS82UcRJ…6BBk27Fi

c68b99b8309869…e17aee6bc2bb33

1 in → 2 out5.9937 XPM226 B

AL3jhqPi…ZgkxPmdG AKCd69dJ…8BiqsTaH

7227de7c05b7e7…57d94066ac0500

1 in → 2 out3.9851 XPM225 B

AP7D9oyF…DfihgmbX Ae7YXEyn…hnSYZsCr

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.

1.158 × 10⁹⁶(97-digit number)

11583546935238464938…94622771506198937600

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

1.158 × 10⁹⁶(97-digit number)

11583546935238464938…94622771506198937599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.158 × 10⁹⁶(97-digit number)

11583546935238464938…94622771506198937601

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

2.316 × 10⁹⁶(97-digit number)

23167093870476929877…89245543012397875199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.316 × 10⁹⁶(97-digit number)

23167093870476929877…89245543012397875201

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

4.633 × 10⁹⁶(97-digit number)

46334187740953859755…78491086024795750399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.633 × 10⁹⁶(97-digit number)

46334187740953859755…78491086024795750401

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

9.266 × 10⁹⁶(97-digit number)

92668375481907719510…56982172049591500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.266 × 10⁹⁶(97-digit number)

92668375481907719510…56982172049591500801

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

1.853 × 10⁹⁷(98-digit number)

18533675096381543902…13964344099183001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.853 × 10⁹⁷(98-digit number)

18533675096381543902…13964344099183001601

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 749441

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 554b051885ffd3201b0401eac116fa20d95b95f098a75c2963775ce8f9548e65

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 #749,441 on Chainz ↗

Block #749,441

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