Home/Chain Registry/Block #3,106,195

Block #3,106,195

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/23/2019, 5:03:33 AM · Difficulty 11.2204 · 3,734,521 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbbbcb7a18ec9b642ff60c4c1fd280f9f8a7130d89a5fdfd05549da337b4e9a8

View on Chainz ↗

Height

#3,106,195

Difficulty

11.220397

Transactions

Size

2.31 KB

Version

Bits

0b386be9

Nonce

664,374,063

Timestamp

3/23/2019, 5:03:33 AM

Confirmations

3,734,521

Merkle Root

cad46c1c6a5f9ba155d9cdc927cb7349e4cebdd426fd99c21d358b16e82038ba

Transactions (4)

Coinbase1412388a8f7f32…3eea1f2f7a2565

1 in → 1 out7.9600 XPM110 B

ARbm48qR…9xQc8DBX

8126dc4a01da6b…dc5a2a6aa5aa21

7 in → 2 out50.0306 XPM912 B

AbXwmGxD…4XXYP765 ARx5pvS5…qXT1H2zv

bbc75119a1df06…1e410e3a2692d5

6 in → 2 out40.9490 XPM798 B

AbXwmGxD…4XXYP765 AKxyVgfv…3DbH8Mh9

7feb5c4bf4e305…230cf7ba570938

3 in → 2 out20.1083 XPM454 B

AXCz3i15…bd3tZodd 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.

2.663 × 10⁹⁸(99-digit number)

26637540848412130512…45546613181312204800

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

2.663 × 10⁹⁸(99-digit number)

26637540848412130512…45546613181312204799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.663 × 10⁹⁸(99-digit number)

26637540848412130512…45546613181312204801

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

5.327 × 10⁹⁸(99-digit number)

53275081696824261024…91093226362624409599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.327 × 10⁹⁸(99-digit number)

53275081696824261024…91093226362624409601

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

1.065 × 10⁹⁹(100-digit number)

10655016339364852204…82186452725248819199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.065 × 10⁹⁹(100-digit number)

10655016339364852204…82186452725248819201

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

2.131 × 10⁹⁹(100-digit number)

21310032678729704409…64372905450497638399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.131 × 10⁹⁹(100-digit number)

21310032678729704409…64372905450497638401

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

4.262 × 10⁹⁹(100-digit number)

42620065357459408819…28745810900995276799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.262 × 10⁹⁹(100-digit number)

42620065357459408819…28745810900995276801

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

8.524 × 10⁹⁹(100-digit number)

85240130714918817639…57491621801990553599

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 3106195

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 dbbbcb7a18ec9b642ff60c4c1fd280f9f8a7130d89a5fdfd05549da337b4e9a8

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 #3,106,195 on Chainz ↗

Block #3,106,195

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