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Block #3,227,420

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/16/2019, 6:20:08 AM · Difficulty 11.0073 · 3,611,600 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9b9241c4f9fa0331d6c4397312327ad379553b61d2397c7e85b98163f79d591

View on Chainz ↗

Height

#3,227,420

Difficulty

11.007292

Transactions

Size

734 B

Version

Bits

0b01dddf

Nonce

1,739,655,229

Timestamp

6/16/2019, 6:20:08 AM

Confirmations

3,611,600

Merkle Root

9430f0470d027fe1eb49eab38230a8f6d5f3315c84d5474b6b96aa33ab967289

Transactions (3)

Coinbase91dbd49925cd60…79a4871721079b

1 in → 1 out8.2600 XPM110 B

AbXwmGxD…4XXYP765

a50230c37c4e31…d235232f69db35

1 in → 2 out8.2200 XPM193 B

AbXwmGxD…4XXYP765 APi57Lph…zJ6tJS5m

af786703d93b53…977f6aa38edbb3

2 in → 2 out10.6402 XPM340 B

AbXwmGxD…4XXYP765 ASUcJnNi…eSt73bFU

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.

1.131 × 10⁹⁶(97-digit number)

11312057257108799327…11561900334287601280

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

1.131 × 10⁹⁶(97-digit number)

11312057257108799327…11561900334287601279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.131 × 10⁹⁶(97-digit number)

11312057257108799327…11561900334287601281

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

2.262 × 10⁹⁶(97-digit number)

22624114514217598654…23123800668575202559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.262 × 10⁹⁶(97-digit number)

22624114514217598654…23123800668575202561

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

4.524 × 10⁹⁶(97-digit number)

45248229028435197309…46247601337150405119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.524 × 10⁹⁶(97-digit number)

45248229028435197309…46247601337150405121

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

9.049 × 10⁹⁶(97-digit number)

90496458056870394619…92495202674300810239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.049 × 10⁹⁶(97-digit number)

90496458056870394619…92495202674300810241

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

1.809 × 10⁹⁷(98-digit number)

18099291611374078923…84990405348601620479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.809 × 10⁹⁷(98-digit number)

18099291611374078923…84990405348601620481

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

3.619 × 10⁹⁷(98-digit number)

36198583222748157847…69980810697203240959

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 3227420

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 e9b9241c4f9fa0331d6c4397312327ad379553b61d2397c7e85b98163f79d591

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 #3,227,420 on Chainz ↗

Block #3,227,420

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