Home/Chain Registry/Block #387,043

Block #387,043

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 8:43:53 PM · Difficulty 10.4140 · 6,413,497 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df34bd3bbf4ae87ebd58855174db53868a7049e48272fe659dbf92a868fc940b

View on Chainz ↗

Height

#387,043

Difficulty

10.413991

Transactions

Size

4.94 KB

Version

Bits

0a69fb4c

Nonce

122,291

Timestamp

2/2/2014, 8:43:53 PM

Confirmations

6,413,497

Merkle Root

6f36c77f156a017010e5d4fb0ec53040b0c19c40e7a930db9df3aa830eb5e28d

Transactions (4)

Coinbase3c47429200d2dd…2ee92989f3c4fd

1 in → 20 out9.2700 XPM743 B

Acs9SHrk…QJSB8SFG APJPNQaM…8nyTxzkW ATLD7BNP…nPjXCb2h AZqjMFvv…G8aw2zC8 AUzEPJFG…kYkA5U9V

ecb854e0175c3c…94b9eb1f7b2e6f

24 in → 2 out74.6057 XPM3.54 KB

AVMPMQgx…TDcCWNZJ ATDtvX88…MuhxANB9

e3d0247c3b21df…ca7389865d903e

1 in → 2 out4.0786 XPM226 B

AL2tVMLd…BmnjW3SP AKyAx5Uo…i4UnLwka

29eb7f01de6a6d…78775771185bc5

2 in → 2 out3.3672 XPM375 B

AFz4gdPG…vn87eren AS2JhWjV…ugC7ZyCT

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.

1.429 × 10⁹⁹(100-digit number)

14293708505583930469…48402140862917734400

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

1.429 × 10⁹⁹(100-digit number)

14293708505583930469…48402140862917734399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.429 × 10⁹⁹(100-digit number)

14293708505583930469…48402140862917734401

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

2.858 × 10⁹⁹(100-digit number)

28587417011167860938…96804281725835468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.858 × 10⁹⁹(100-digit number)

28587417011167860938…96804281725835468801

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

5.717 × 10⁹⁹(100-digit number)

57174834022335721876…93608563451670937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.717 × 10⁹⁹(100-digit number)

57174834022335721876…93608563451670937601

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

1.143 × 10¹⁰⁰(101-digit number)

11434966804467144375…87217126903341875199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.143 × 10¹⁰⁰(101-digit number)

11434966804467144375…87217126903341875201

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

2.286 × 10¹⁰⁰(101-digit number)

22869933608934288750…74434253806683750399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.286 × 10¹⁰⁰(101-digit number)

22869933608934288750…74434253806683750401

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 387043

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 df34bd3bbf4ae87ebd58855174db53868a7049e48272fe659dbf92a868fc940b

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 #387,043 on Chainz ↗