Home/Chain Registry/Block #2,471,119

Block #2,471,119

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/13/2018, 1:21:54 PM · Difficulty 10.9617 · 4,367,393 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2937a3575febe798fb182639d978bebafe9d97d2b8e34d3c8ce5a67fa07a8697

View on Chainz ↗

Height

#2,471,119

Difficulty

10.961660

Transactions

Size

2.02 KB

Version

Bits

0af62f59

Nonce

596,881,395

Timestamp

1/13/2018, 1:21:54 PM

Confirmations

4,367,393

Merkle Root

9a9132c88ef7e7cf58ebc4b4b655863592e439eda123d401e1ed033023f9b855

Transactions (3)

Coinbase20754b18c57cd8…2293df63883980

1 in → 1 out8.3500 XPM109 B

ATvjigwj…UGNMgW6X

40c9b2b3b9bac8…d442cad370323b

1 in → 3 out32.1487 XPM260 B

AHPmXZeL…hGP7XivN AQvQPfam…afZnLSkq APBM2w7U…Qx6F7p89

7055004def5da5…7707afea38a520

11 in → 1 out20.0000 XPM1.57 KB

ARezZb4y…FxP7ivbi

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.

8.869 × 10⁹⁴(95-digit number)

88693289482424214466…21102327132402499680

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

8.869 × 10⁹⁴(95-digit number)

88693289482424214466…21102327132402499679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.869 × 10⁹⁴(95-digit number)

88693289482424214466…21102327132402499681

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

1.773 × 10⁹⁵(96-digit number)

17738657896484842893…42204654264804999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.773 × 10⁹⁵(96-digit number)

17738657896484842893…42204654264804999361

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

3.547 × 10⁹⁵(96-digit number)

35477315792969685786…84409308529609998719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.547 × 10⁹⁵(96-digit number)

35477315792969685786…84409308529609998721

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

7.095 × 10⁹⁵(96-digit number)

70954631585939371572…68818617059219997439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.095 × 10⁹⁵(96-digit number)

70954631585939371572…68818617059219997441

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

1.419 × 10⁹⁶(97-digit number)

14190926317187874314…37637234118439994879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.419 × 10⁹⁶(97-digit number)

14190926317187874314…37637234118439994881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.838 × 10⁹⁶(97-digit number)

28381852634375748629…75274468236879989759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2471119

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 2937a3575febe798fb182639d978bebafe9d97d2b8e34d3c8ce5a67fa07a8697

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 #2,471,119 on Chainz ↗

Block #2,471,119

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