Home/Chain Registry/Block #2,169,811

Block #2,169,811

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2017, 3:35:55 AM · Difficulty 10.9008 · 4,673,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1e1049a0c7f40d9992ec08810ff508d2841d4643146413fc99215e126e147c6

View on Chainz ↗

Height

#2,169,811

Difficulty

10.900763

Transactions

Size

1.07 KB

Version

Bits

0ae6986c

Nonce

1,148,213,872

Timestamp

6/21/2017, 3:35:55 AM

Confirmations

4,673,255

Merkle Root

efc20beb6a8fb7adb5b69136f2c13a189156f1635af65b1a065cd55970982130

Transactions (3)

Coinbase2cfd3ce92576eb…2894e5b49ddf3b

1 in → 1 out8.4400 XPM110 B

AcGDrJjA…jbj4RmNN

b4b8eec339126d…d5840c2d9e38f1

1 in → 2 out347610.4268 XPM226 B

AaZoWCHB…mjEezUPQ ANx9rhLy…JwGoFiRy

6655bce94af91d…7f6807e6b134a5

4 in → 2 out2000.0146 XPM669 B

ARaNCeSx…b8M3uhxY AQQvPXHf…5xtiQ7xi

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.

2.227 × 10⁹⁸(99-digit number)

22271927848523312667…98271060703403048960

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

2.227 × 10⁹⁸(99-digit number)

22271927848523312667…98271060703403048959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.227 × 10⁹⁸(99-digit number)

22271927848523312667…98271060703403048961

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

4.454 × 10⁹⁸(99-digit number)

44543855697046625334…96542121406806097919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.454 × 10⁹⁸(99-digit number)

44543855697046625334…96542121406806097921

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

8.908 × 10⁹⁸(99-digit number)

89087711394093250669…93084242813612195839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.908 × 10⁹⁸(99-digit number)

89087711394093250669…93084242813612195841

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

1.781 × 10⁹⁹(100-digit number)

17817542278818650133…86168485627224391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.781 × 10⁹⁹(100-digit number)

17817542278818650133…86168485627224391681

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

3.563 × 10⁹⁹(100-digit number)

35635084557637300267…72336971254448783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.563 × 10⁹⁹(100-digit number)

35635084557637300267…72336971254448783361

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 2169811

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 e1e1049a0c7f40d9992ec08810ff508d2841d4643146413fc99215e126e147c6

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 #2,169,811 on Chainz ↗

Block #2,169,811

Cookie Preferences