Home/Chain Registry/Block #252,674

Block #252,674

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 5:19:35 PM · Difficulty 9.9713 · 6,538,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cba30ae4020088b73ee9f7bb695d93dac16b923b974c57f1b0d63df612cda9e3

View on Chainz ↗

Height

#252,674

Difficulty

9.971324

Transactions

Size

228 B

Version

Bits

09f8a8ab

Nonce

5,953

Timestamp

11/9/2013, 5:19:35 PM

Confirmations

6,538,385

Merkle Root

8057151ef78d3b0417907d584db204715faac6848f3f4a450ba8d98d3c9f6173

Transactions (1)

Coinbase8057151ef78d3b…a8d98d3c9f6173

1 in → 2 out10.0400 XPM137 B

ARmAMwyu…P7Kn74ZT ASNt3cJa…L5zCqAYM

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.

6.745 × 10⁹⁶(97-digit number)

67459264373967921774…20201515420896222720

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

6.745 × 10⁹⁶(97-digit number)

67459264373967921774…20201515420896222719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.745 × 10⁹⁶(97-digit number)

67459264373967921774…20201515420896222721

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

1.349 × 10⁹⁷(98-digit number)

13491852874793584354…40403030841792445439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.349 × 10⁹⁷(98-digit number)

13491852874793584354…40403030841792445441

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

2.698 × 10⁹⁷(98-digit number)

26983705749587168709…80806061683584890879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.698 × 10⁹⁷(98-digit number)

26983705749587168709…80806061683584890881

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

5.396 × 10⁹⁷(98-digit number)

53967411499174337419…61612123367169781759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.396 × 10⁹⁷(98-digit number)

53967411499174337419…61612123367169781761

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

1.079 × 10⁹⁸(99-digit number)

10793482299834867483…23224246734339563519

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 252674

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 cba30ae4020088b73ee9f7bb695d93dac16b923b974c57f1b0d63df612cda9e3

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 #252,674 on Chainz ↗