Home/Chain Registry/Block #2,131,296

Block #2,131,296

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2017, 12:22:31 AM · Difficulty 10.9101 · 4,711,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3bef67fb142e1dceb394122b897023c05a2cf0af4ced85de0e0abf40bddd9852

View on Chainz ↗

Height

#2,131,296

Difficulty

10.910128

Transactions

Size

654 B

Version

Bits

0ae8fe2d

Nonce

549,871,656

Timestamp

5/25/2017, 12:22:31 AM

Confirmations

4,711,580

Merkle Root

f9fcdd95a8a43bf76f81fed255234adf93c055333838ca4c8b212ed9ba4db7a0

Transactions (3)

Coinbase7586c748bb316e…cea7f6ac844fb9

1 in → 1 out8.4100 XPM110 B

AS5si5G3…hsDC4exW

93e51e982a52e7…91230cb6fc2a75

1 in → 2 out193769.9000 XPM227 B

AHReQqRi…EvE5GyCq AYLHmLo2…rjWjYkjQ

add742a8eb992f…458561c260fdfd

1 in → 2 out82974.4647 XPM227 B

ATWcaZVY…aG8EKwNf AG71SyVZ…skVYBbj4

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.

4.646 × 10⁹⁵(96-digit number)

46466379260065312948…93828571256567234560

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

4.646 × 10⁹⁵(96-digit number)

46466379260065312948…93828571256567234559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.646 × 10⁹⁵(96-digit number)

46466379260065312948…93828571256567234561

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

9.293 × 10⁹⁵(96-digit number)

92932758520130625896…87657142513134469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.293 × 10⁹⁵(96-digit number)

92932758520130625896…87657142513134469121

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

1.858 × 10⁹⁶(97-digit number)

18586551704026125179…75314285026268938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.858 × 10⁹⁶(97-digit number)

18586551704026125179…75314285026268938241

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

3.717 × 10⁹⁶(97-digit number)

37173103408052250358…50628570052537876479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.717 × 10⁹⁶(97-digit number)

37173103408052250358…50628570052537876481

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

7.434 × 10⁹⁶(97-digit number)

74346206816104500717…01257140105075752959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.434 × 10⁹⁶(97-digit number)

74346206816104500717…01257140105075752961

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 2131296

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 3bef67fb142e1dceb394122b897023c05a2cf0af4ced85de0e0abf40bddd9852

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 #2,131,296 on Chainz ↗

Block #2,131,296

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