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Block #53,716

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 4:40:05 PM · Difficulty 8.9265 · 6,771,919 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d4e5c75c33d795f6b2605e1f39c5965b76a310a636603e9cd311bb0269e55ec5

View on Chainz ↗

Height

#53,716

Difficulty

8.926492

Transactions

Size

206 B

Version

Bits

08ed2e8f

Nonce

669

Timestamp

7/16/2013, 4:40:05 PM

Confirmations

6,771,919

Merkle Root

40184b6432b3b281f0bd083bc60cfae2a6b1dcce1ddb037e99ecfc4fb3ab6cde

Transactions (1)

Coinbase40184b6432b3b2…ecfc4fb3ab6cde

1 in → 1 out12.5300 XPM110 B

AZakk5h5…giTZcejN

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.

1.954 × 10¹⁰⁹(110-digit number)

19544299268369255107…47226035371014896800

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

1.954 × 10¹⁰⁹(110-digit number)

19544299268369255107…47226035371014896799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.954 × 10¹⁰⁹(110-digit number)

19544299268369255107…47226035371014896801

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

3.908 × 10¹⁰⁹(110-digit number)

39088598536738510215…94452070742029793599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.908 × 10¹⁰⁹(110-digit number)

39088598536738510215…94452070742029793601

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

7.817 × 10¹⁰⁹(110-digit number)

78177197073477020431…88904141484059587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.817 × 10¹⁰⁹(110-digit number)

78177197073477020431…88904141484059587201

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

1.563 × 10¹¹⁰(111-digit number)

15635439414695404086…77808282968119174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.563 × 10¹¹⁰(111-digit number)

15635439414695404086…77808282968119174401

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 53716

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 d4e5c75c33d795f6b2605e1f39c5965b76a310a636603e9cd311bb0269e55ec5

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 #53,716 on Chainz ↗

Block #53,716

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