Home/Chain Registry/Block #3,079,222

Block #3,079,222

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/5/2019, 7:30:20 AM · Difficulty 11.0098 · 3,761,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7f590fa941ecac3aaa92772499fd134048440874124c6c0d17b5ebe4ca10629

View on Chainz ↗

Height

#3,079,222

Difficulty

11.009780

Transactions

Size

997 B

Version

Bits

0b0280e9

Nonce

1,787,007,530

Timestamp

3/5/2019, 7:30:20 AM

Confirmations

3,761,758

Merkle Root

97bd30e2a9fa8415ffe9d961a96c02cc0ae0c618f1662d1c32e14789f2d1fae6

Transactions (3)

Coinbasecc1b402f076bba…b26056145c33eb

1 in → 1 out8.2600 XPM109 B

AbXwmGxD…4XXYP765

017e94f4ec8376…3c6f376decb223

2 in → 2 out16.4300 XPM307 B

AYwhSvcj…ZTBPYo3R AUWdrCrB…8KBu9BWe

308ef79f2a23ac…a34a728a3d2807

3 in → 2 out10.3300 XPM490 B

APVKWthF…PMMxwRoz AG7gRXuT…YjjNWNPm

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.

1.644 × 10⁹⁷(98-digit number)

16444960801505903826…38919145603163955200

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

1.644 × 10⁹⁷(98-digit number)

16444960801505903826…38919145603163955199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.644 × 10⁹⁷(98-digit number)

16444960801505903826…38919145603163955201

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

3.288 × 10⁹⁷(98-digit number)

32889921603011807653…77838291206327910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.288 × 10⁹⁷(98-digit number)

32889921603011807653…77838291206327910401

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

6.577 × 10⁹⁷(98-digit number)

65779843206023615307…55676582412655820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.577 × 10⁹⁷(98-digit number)

65779843206023615307…55676582412655820801

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

1.315 × 10⁹⁸(99-digit number)

13155968641204723061…11353164825311641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.315 × 10⁹⁸(99-digit number)

13155968641204723061…11353164825311641601

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

2.631 × 10⁹⁸(99-digit number)

26311937282409446123…22706329650623283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.631 × 10⁹⁸(99-digit number)

26311937282409446123…22706329650623283201

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

5.262 × 10⁹⁸(99-digit number)

52623874564818892246…45412659301246566399

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 3079222

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 c7f590fa941ecac3aaa92772499fd134048440874124c6c0d17b5ebe4ca10629

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 #3,079,222 on Chainz ↗

Block #3,079,222

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