Home/Chain Registry/Block #2,261,456

Block #2,261,456

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/21/2017, 9:48:19 AM · Difficulty 10.9523 · 4,580,697 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

624cb6020804be7202b4e4f7abd7eca1b6fe472bb61c4dd1fe7c19131e6ed882

View on Chainz ↗

Height

#2,261,456

Difficulty

10.952251

Transactions

Size

1.43 KB

Version

Bits

0af3c6b4

Nonce

498,969,461

Timestamp

8/21/2017, 9:48:19 AM

Confirmations

4,580,697

Merkle Root

4873ec95d3102bf8ebf0afafd317f6ad141cccded3f1d09af5532211964e787e

Transactions (2)

Coinbase2a1e091ed1a2f2…9332aa10c60d23

1 in → 1 out8.3400 XPM110 B

AFzETwAP…ZcPo4n3J

d77c052e24a08d…e8c4a0a3ecce03

8 in → 2 out413.3543 XPM1.23 KB

ASnzm9S9…A3PBVhJE AVvCESHa…pYwkriph

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.

9.393 × 10⁹⁷(98-digit number)

93931245512677108520…32299304676434001920

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

9.393 × 10⁹⁷(98-digit number)

93931245512677108520…32299304676434001919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.393 × 10⁹⁷(98-digit number)

93931245512677108520…32299304676434001921

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

1.878 × 10⁹⁸(99-digit number)

18786249102535421704…64598609352868003839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.878 × 10⁹⁸(99-digit number)

18786249102535421704…64598609352868003841

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

3.757 × 10⁹⁸(99-digit number)

37572498205070843408…29197218705736007679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.757 × 10⁹⁸(99-digit number)

37572498205070843408…29197218705736007681

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

7.514 × 10⁹⁸(99-digit number)

75144996410141686816…58394437411472015359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.514 × 10⁹⁸(99-digit number)

75144996410141686816…58394437411472015361

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

1.502 × 10⁹⁹(100-digit number)

15028999282028337363…16788874822944030719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.502 × 10⁹⁹(100-digit number)

15028999282028337363…16788874822944030721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.005 × 10⁹⁹(100-digit number)

30057998564056674726…33577749645888061439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2261456

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 624cb6020804be7202b4e4f7abd7eca1b6fe472bb61c4dd1fe7c19131e6ed882

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 #2,261,456 on Chainz ↗

Block #2,261,456

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