Home/Chain Registry/Block #3,082,611

Block #3,082,611

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/7/2019, 3:05:05 PM · Difficulty 11.0211 · 3,761,359 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83d3a1b386af952e86f3b2abc48ad5cec6070bbbdca080038fd1c3e805c6a611

View on Chainz ↗

Height

#3,082,611

Difficulty

11.021064

Transactions

Size

1.59 KB

Version

Bits

0b05646e

Nonce

6,335,716

Timestamp

3/7/2019, 3:05:05 PM

Confirmations

3,761,359

Merkle Root

1bed6387447e99c8fbdeff7461d1c8e346d560113343485b64e53d028a088207

Transactions (4)

Coinbaseeb00d0cc5813b6…0d616c3a9384b3

1 in → 1 out8.2500 XPM110 B

AUhjokok…k5m93PZR

42c4680a35f290…e0e09a1edabe60

2 in → 2 out2438.4900 XPM374 B

AeTHTL7A…vT1872bk AZiSbxmk…W3DeJU8E

55df444b0112ba…9c07b60364fd4d

3 in → 2 out20.6636 XPM455 B

AbXwmGxD…4XXYP765 AXCz3i15…bd3tZodd

a9c8fe0cca0cde…a480b2a4854e01

4 in → 2 out20.1788 XPM600 B

AXgNzcfF…AhQqtGB2 AbXwmGxD…4XXYP765

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.

2.189 × 10⁹⁴(95-digit number)

21895689664758584437…12700893889232871280

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

2.189 × 10⁹⁴(95-digit number)

21895689664758584437…12700893889232871279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.189 × 10⁹⁴(95-digit number)

21895689664758584437…12700893889232871281

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

4.379 × 10⁹⁴(95-digit number)

43791379329517168875…25401787778465742559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.379 × 10⁹⁴(95-digit number)

43791379329517168875…25401787778465742561

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

8.758 × 10⁹⁴(95-digit number)

87582758659034337751…50803575556931485119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.758 × 10⁹⁴(95-digit number)

87582758659034337751…50803575556931485121

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

1.751 × 10⁹⁵(96-digit number)

17516551731806867550…01607151113862970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.751 × 10⁹⁵(96-digit number)

17516551731806867550…01607151113862970241

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

3.503 × 10⁹⁵(96-digit number)

35033103463613735100…03214302227725940479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.503 × 10⁹⁵(96-digit number)

35033103463613735100…03214302227725940481

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

7.006 × 10⁹⁵(96-digit number)

70066206927227470200…06428604455451880959

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 3082611

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 83d3a1b386af952e86f3b2abc48ad5cec6070bbbdca080038fd1c3e805c6a611

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 #3,082,611 on Chainz ↗

Block #3,082,611

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