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Block #2,111,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2017, 12:40:56 PM · Difficulty 10.9029 · 4,731,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a52995cc2d115ea5dfb7b634d90e4d34d6d344b7aaf9c6bcb8ed691954bd93b

View on Chainz ↗

Height

#2,111,522

Difficulty

10.902923

Transactions

Size

425 B

Version

Bits

0ae725f4

Nonce

872,477,592

Timestamp

5/11/2017, 12:40:56 PM

Confirmations

4,731,052

Merkle Root

4b9cc5ea3d33bd861f8fcad7e93314ed38137f1ceeed0f30979a23de31feadd3

Transactions (2)

Coinbase2f641cbabdd018…90c6e305c58085

1 in → 1 out8.4100 XPM109 B

AVxKRBWf…BQrXKcq6

46668aef7af9fd…2101751e7256b2

1 in → 2 out190901.5883 XPM226 B

AQNouH96…TqowgaMQ ATjeKjRU…dEVNyPPF

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.

3.769 × 10⁹⁴(95-digit number)

37691266982759909642…78538002758951349920

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

3.769 × 10⁹⁴(95-digit number)

37691266982759909642…78538002758951349919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.769 × 10⁹⁴(95-digit number)

37691266982759909642…78538002758951349921

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

7.538 × 10⁹⁴(95-digit number)

75382533965519819284…57076005517902699839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.538 × 10⁹⁴(95-digit number)

75382533965519819284…57076005517902699841

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

1.507 × 10⁹⁵(96-digit number)

15076506793103963856…14152011035805399679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.507 × 10⁹⁵(96-digit number)

15076506793103963856…14152011035805399681

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

3.015 × 10⁹⁵(96-digit number)

30153013586207927713…28304022071610799359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.015 × 10⁹⁵(96-digit number)

30153013586207927713…28304022071610799361

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

6.030 × 10⁹⁵(96-digit number)

60306027172415855427…56608044143221598719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.030 × 10⁹⁵(96-digit number)

60306027172415855427…56608044143221598721

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 2111522

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 8a52995cc2d115ea5dfb7b634d90e4d34d6d344b7aaf9c6bcb8ed691954bd93b

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 #2,111,522 on Chainz ↗

Block #2,111,522

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