Home/Chain Registry/Block #75,345

Block #75,345

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 3:57:29 PM · Difficulty 8.9961 · 6,717,268 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e0e23e4897206a428dbda37dcb026e5e2827dae65de16849d2af47f5ef69248

View on Chainz ↗

Height

#75,345

Difficulty

8.996056

Transactions

Size

3.97 KB

Version

Bits

08fefd8e

Nonce

372

Timestamp

7/21/2013, 3:57:29 PM

Confirmations

6,717,268

Merkle Root

3e4ff29fe5ddf57e3efc0cb6a195269f66c53697935940322ae5ed8cc758e9dd

Transactions (2)

Coinbase245aa93c4eb8c6…264921120032ce

1 in → 1 out12.3800 XPM110 B

AVQxbFsH…KG2vYXbz

2fbeef9f1ba70f…58c1023e4dd0d9

33 in → 1 out383.0000 XPM3.78 KB

AK9oER6E…EXH5jCFs

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.

7.550 × 10⁹⁴(95-digit number)

75508077005851939676…91005235062421718340

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

7.550 × 10⁹⁴(95-digit number)

75508077005851939676…91005235062421718339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.550 × 10⁹⁴(95-digit number)

75508077005851939676…91005235062421718341

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

1.510 × 10⁹⁵(96-digit number)

15101615401170387935…82010470124843436679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.510 × 10⁹⁵(96-digit number)

15101615401170387935…82010470124843436681

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

3.020 × 10⁹⁵(96-digit number)

30203230802340775870…64020940249686873359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.020 × 10⁹⁵(96-digit number)

30203230802340775870…64020940249686873361

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

6.040 × 10⁹⁵(96-digit number)

60406461604681551740…28041880499373746719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.040 × 10⁹⁵(96-digit number)

60406461604681551740…28041880499373746721

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

1.208 × 10⁹⁶(97-digit number)

12081292320936310348…56083760998747493439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 75345

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 2e0e23e4897206a428dbda37dcb026e5e2827dae65de16849d2af47f5ef69248

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 #75,345 on Chainz ↗