Home/Chain Registry/Block #2,932,968

Block #2,932,968

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/21/2018, 12:48:47 PM · Difficulty 11.3974 · 3,898,907 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9aed1ffa6604e0bb8c6c9ad803b7b74e9a3244f55bc2c243de453b0987991ff8

View on Chainz ↗

Height

#2,932,968

Difficulty

11.397393

Transactions

Size

1.16 KB

Version

Bits

0b65bb8a

Nonce

639,085,261

Timestamp

11/21/2018, 12:48:47 PM

Confirmations

3,898,907

Merkle Root

22d896f7ac293014ed9566e46ba2f25e854c037bdf374fb02d78ed98e19db510

Transactions (4)

Coinbasee12980b7849010…1f241f900e8317

1 in → 1 out7.7200 XPM110 B

AUMQRepm…tAfKmdW1

a1da9efac9aed5…93fe5beaf124f0

2 in → 2 out15.4500 XPM305 B

AN2Y8Cst…Mcivy8n7 APVKWthF…PMMxwRoz

93a7352aa994a9…15829c5383bb96

2 in → 2 out15.3900 XPM307 B

AKtg5M5J…UY3VCdzE AHZxSRSE…GnuQtUtD

9e7731f0ebbab9…b08b213e6a17f3

2 in → 2 out10.8300 XPM374 B

AZrrkiXx…HEKyFuAh ATTNPD3w…udMBvYq2

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.

3.983 × 10⁹⁴(95-digit number)

39832883342133692278…31892784366397237600

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

3.983 × 10⁹⁴(95-digit number)

39832883342133692278…31892784366397237599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.983 × 10⁹⁴(95-digit number)

39832883342133692278…31892784366397237601

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

7.966 × 10⁹⁴(95-digit number)

79665766684267384557…63785568732794475199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.966 × 10⁹⁴(95-digit number)

79665766684267384557…63785568732794475201

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

1.593 × 10⁹⁵(96-digit number)

15933153336853476911…27571137465588950399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.593 × 10⁹⁵(96-digit number)

15933153336853476911…27571137465588950401

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

3.186 × 10⁹⁵(96-digit number)

31866306673706953822…55142274931177900799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.186 × 10⁹⁵(96-digit number)

31866306673706953822…55142274931177900801

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

6.373 × 10⁹⁵(96-digit number)

63732613347413907645…10284549862355801599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.373 × 10⁹⁵(96-digit number)

63732613347413907645…10284549862355801601

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

1.274 × 10⁹⁶(97-digit number)

12746522669482781529…20569099724711603199

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 2932968

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 9aed1ffa6604e0bb8c6c9ad803b7b74e9a3244f55bc2c243de453b0987991ff8

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 #2,932,968 on Chainz ↗

Block #2,932,968

Cookie Preferences