Home/Chain Registry/Block #252,581

Block #252,581

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 4:10:19 PM · Difficulty 9.9712 · 6,547,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

484d7941e591bb978378911ec1fb599efbe9a47dca8d9ea9d072b8c495c42ec9

View on Chainz ↗

Height

#252,581

Difficulty

9.971212

Transactions

Size

2.21 KB

Version

Bits

09f8a15c

Nonce

8,146

Timestamp

11/9/2013, 4:10:19 PM

Confirmations

6,547,839

Merkle Root

e78db6c3ae83cb5d25f9d5d1e92dcd45675f3f08e909936a0ae35a7ced8ba977

Transactions (1)

Coinbasee78db6c3ae83cb…e35a7ced8ba977

1 in → 62 out10.0100 XPM2.12 KB

Aaf3CsqS…k1Eu3vmJ AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU AJzWx2VD…j4ZSMit5

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.

6.565 × 10⁹⁶(97-digit number)

65657390444872509392…17771243571348319080

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

6.565 × 10⁹⁶(97-digit number)

65657390444872509392…17771243571348319079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.565 × 10⁹⁶(97-digit number)

65657390444872509392…17771243571348319081

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

1.313 × 10⁹⁷(98-digit number)

13131478088974501878…35542487142696638159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.313 × 10⁹⁷(98-digit number)

13131478088974501878…35542487142696638161

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

2.626 × 10⁹⁷(98-digit number)

26262956177949003757…71084974285393276319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.626 × 10⁹⁷(98-digit number)

26262956177949003757…71084974285393276321

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

5.252 × 10⁹⁷(98-digit number)

52525912355898007514…42169948570786552639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.252 × 10⁹⁷(98-digit number)

52525912355898007514…42169948570786552641

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

1.050 × 10⁹⁸(99-digit number)

10505182471179601502…84339897141573105279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.050 × 10⁹⁸(99-digit number)

10505182471179601502…84339897141573105281

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 252581

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 484d7941e591bb978378911ec1fb599efbe9a47dca8d9ea9d072b8c495c42ec9

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 #252,581 on Chainz ↗