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Block #49,646

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 9:23:51 PM · Difficulty 8.8688 · 6,740,218 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7825db878be63c500350e6c3757c23e1735414f7dd44f1e931215af85453b152

View on Chainz ↗

Height

#49,646

Difficulty

8.868785

Transactions

Size

198 B

Version

Bits

08de68ae

Nonce

424

Timestamp

7/15/2013, 9:23:51 PM

Confirmations

6,740,218

Merkle Root

5f626b14a44cd97c321f1702fa459503bafa9c6cf18bb8f16cc4d58b50053c05

Transactions (1)

Coinbase5f626b14a44cd9…c4d58b50053c05

1 in → 1 out12.7000 XPM109 B

AQeawDDL…QZiJhBPg

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.

3.120 × 10⁹³(94-digit number)

31203309092441403821…56371150138011352960

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

3.120 × 10⁹³(94-digit number)

31203309092441403821…56371150138011352959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.120 × 10⁹³(94-digit number)

31203309092441403821…56371150138011352961

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

6.240 × 10⁹³(94-digit number)

62406618184882807642…12742300276022705919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.240 × 10⁹³(94-digit number)

62406618184882807642…12742300276022705921

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

1.248 × 10⁹⁴(95-digit number)

12481323636976561528…25484600552045411839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.248 × 10⁹⁴(95-digit number)

12481323636976561528…25484600552045411841

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

2.496 × 10⁹⁴(95-digit number)

24962647273953123057…50969201104090823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.496 × 10⁹⁴(95-digit number)

24962647273953123057…50969201104090823681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 49646

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 7825db878be63c500350e6c3757c23e1735414f7dd44f1e931215af85453b152

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 #49,646 on Chainz ↗