Home/Chain Registry/Block #424,643

Block #424,643

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/1/2014, 8:53:11 AM · Difficulty 10.3607 · 6,373,973 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf4d5fc93b89c7c37cf05df1ef255d784b5806d5f12a07386220950dd3989299

View on Chainz ↗

Height

#424,643

Difficulty

10.360742

Transactions

Size

970 B

Version

Bits

0a5c5995

Nonce

4,737

Timestamp

3/1/2014, 8:53:11 AM

Confirmations

6,373,973

Merkle Root

2438b54dbcd90916bec405882d85f614093e719104234a2377d49e69d8c0d4c5

Transactions (1)

Coinbase2438b54dbcd909…d49e69d8c0d4c5

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

7.480 × 10⁹⁶(97-digit number)

74808989534051945594…56210837314432918000

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

7.480 × 10⁹⁶(97-digit number)

74808989534051945594…56210837314432917999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.480 × 10⁹⁶(97-digit number)

74808989534051945594…56210837314432918001

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

1.496 × 10⁹⁷(98-digit number)

14961797906810389118…12421674628865835999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.496 × 10⁹⁷(98-digit number)

14961797906810389118…12421674628865836001

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

2.992 × 10⁹⁷(98-digit number)

29923595813620778237…24843349257731671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.992 × 10⁹⁷(98-digit number)

29923595813620778237…24843349257731672001

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

5.984 × 10⁹⁷(98-digit number)

59847191627241556475…49686698515463343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.984 × 10⁹⁷(98-digit number)

59847191627241556475…49686698515463344001

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

1.196 × 10⁹⁸(99-digit number)

11969438325448311295…99373397030926687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.196 × 10⁹⁸(99-digit number)

11969438325448311295…99373397030926688001

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 424643

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 bf4d5fc93b89c7c37cf05df1ef255d784b5806d5f12a07386220950dd3989299

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 #424,643 on Chainz ↗