Home/Chain Registry/Block #384,483

Block #384,483

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 3:54:07 AM · Difficulty 10.4002 · 6,442,216 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5297e2d01e9bac052dd53052f0fd31a36cfa40fa280c98940fb09420bee3d3e

View on Chainz ↗

Height

#384,483

Difficulty

10.400196

Transactions

Size

1.00 KB

Version

Bits

0a667344

Nonce

12,825,093

Timestamp

2/1/2014, 3:54:07 AM

Confirmations

6,442,216

Merkle Root

0f996d20bdbdfb96ce60280c79ef530069aa5a0aa246736bb26b1b5b360d3fb8

Transactions (4)

Coinbasec4776ece620f96…e08286a97a909c

1 in → 1 out9.2600 XPM109 B

Aa1F84tb…k4k34Xz5

14c7aabc070c16…80c2bee4664eac

2 in → 2 out31.7395 XPM374 B

ATrnQSUS…9uRmywww AUCd3RmJ…QBRMCp88

0461486f30b901…aacbc7211c5250

1 in → 2 out2.1130 XPM226 B

AWNNSGAK…akW8k63B AXRc2m5s…zwKHBr98

b772c5cdf7675d…83c7fc405bdeea

1 in → 2 out1.1081 XPM226 B

AUAfYcmQ…B3DywuZK AN6sR6WK…i9uEKTaS

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.

1.066 × 10⁹⁶(97-digit number)

10666766413736612999…65452822435217743360

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

1.066 × 10⁹⁶(97-digit number)

10666766413736612999…65452822435217743359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.066 × 10⁹⁶(97-digit number)

10666766413736612999…65452822435217743361

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

2.133 × 10⁹⁶(97-digit number)

21333532827473225999…30905644870435486719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.133 × 10⁹⁶(97-digit number)

21333532827473225999…30905644870435486721

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

4.266 × 10⁹⁶(97-digit number)

42667065654946451999…61811289740870973439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.266 × 10⁹⁶(97-digit number)

42667065654946451999…61811289740870973441

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

8.533 × 10⁹⁶(97-digit number)

85334131309892903999…23622579481741946879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.533 × 10⁹⁶(97-digit number)

85334131309892903999…23622579481741946881

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

1.706 × 10⁹⁷(98-digit number)

17066826261978580799…47245158963483893759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.706 × 10⁹⁷(98-digit number)

17066826261978580799…47245158963483893761

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 384483

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 b5297e2d01e9bac052dd53052f0fd31a36cfa40fa280c98940fb09420bee3d3e

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 #384,483 on Chainz ↗

Block #384,483

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