Home/Chain Registry/Block #43,028

Block #43,028

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 7:58:59 PM · Difficulty 8.6392 · 6,746,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d39f415111a3b40ec9013429856c215f9aa3f30b280ddf6a1ee080a5c3460fa

View on Chainz ↗

Height

#43,028

Difficulty

8.639206

Transactions

Size

619 B

Version

Bits

08a3a301

Nonce

Timestamp

7/14/2013, 7:58:59 PM

Confirmations

6,746,835

Merkle Root

44b6658edc50e84912a29dc616288d9ff22ea730c4bc6905129ef142ff5ef089

Transactions (2)

Coinbase225417de8a9d23…228a1959bc214c

1 in → 1 out13.3900 XPM110 B

AXPx32rf…uuWLcuee

02afc80ec08661…a3adbfd34ab17f

3 in → 1 out29.2100 XPM419 B

AREJRekG…a8dWbE8j

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.

4.793 × 10⁹⁵(96-digit number)

47934398541998572454…41260969115077055250

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

4.793 × 10⁹⁵(96-digit number)

47934398541998572454…41260969115077055249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.793 × 10⁹⁵(96-digit number)

47934398541998572454…41260969115077055251

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

9.586 × 10⁹⁵(96-digit number)

95868797083997144909…82521938230154110499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.586 × 10⁹⁵(96-digit number)

95868797083997144909…82521938230154110501

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

1.917 × 10⁹⁶(97-digit number)

19173759416799428981…65043876460308220999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.917 × 10⁹⁶(97-digit number)

19173759416799428981…65043876460308221001

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

3.834 × 10⁹⁶(97-digit number)

38347518833598857963…30087752920616441999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.834 × 10⁹⁶(97-digit number)

38347518833598857963…30087752920616442001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

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 43028

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 6d39f415111a3b40ec9013429856c215f9aa3f30b280ddf6a1ee080a5c3460fa

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 #43,028 on Chainz ↗