Home/Chain Registry/Block #2,676,636

Block #2,676,636

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2018, 12:25:43 AM · Difficulty 11.6979 · 4,165,219 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5589fb9219dca701a63e8f9c9870d816461ad7e4561b01c00354aa1c88458626

View on Chainz ↗

Height

#2,676,636

Difficulty

11.697927

Transactions

Size

845 B

Version

Bits

0bb2ab56

Nonce

2,106,283,287

Timestamp

5/25/2018, 12:25:43 AM

Confirmations

4,165,219

Merkle Root

beaa80134f0e16f5e8a347bea6ccacdaf368b8d084d73896c6506b1cfd80d38d

Transactions (4)

Coinbaseba8d93dc57da96…15fdbf53a5193d

1 in → 1 out7.3300 XPM110 B

AS5hYWcf…qFTE9iEu

3963869d90b035…c8789137a3b977

1 in → 2 out7.2900 XPM191 B

ANxNfXmZ…4p5PaHCM AJhH7aby…GECoV2Yx

c291d2537fbf60…53188ab91bb1c8

1 in → 2 out2.3290 XPM227 B

AW2Qk6h2…JKWNC5Aa Af4eUqWS…B31dCoG1

386ce268ab796d…d3066c47f163e8

1 in → 2 out2.2186 XPM226 B

ALeTJ8da…6KLwvMJC AYDuNsYz…Mtn61d6g

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.

3.021 × 10⁹⁶(97-digit number)

30211099204902186743…03220771682650910720

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

3.021 × 10⁹⁶(97-digit number)

30211099204902186743…03220771682650910719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.021 × 10⁹⁶(97-digit number)

30211099204902186743…03220771682650910721

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

6.042 × 10⁹⁶(97-digit number)

60422198409804373486…06441543365301821439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.042 × 10⁹⁶(97-digit number)

60422198409804373486…06441543365301821441

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

1.208 × 10⁹⁷(98-digit number)

12084439681960874697…12883086730603642879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.208 × 10⁹⁷(98-digit number)

12084439681960874697…12883086730603642881

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

2.416 × 10⁹⁷(98-digit number)

24168879363921749394…25766173461207285759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.416 × 10⁹⁷(98-digit number)

24168879363921749394…25766173461207285761

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

4.833 × 10⁹⁷(98-digit number)

48337758727843498789…51532346922414571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.833 × 10⁹⁷(98-digit number)

48337758727843498789…51532346922414571521

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

9.667 × 10⁹⁷(98-digit number)

96675517455686997578…03064693844829143039

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 2676636

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 5589fb9219dca701a63e8f9c9870d816461ad7e4561b01c00354aa1c88458626

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 #2,676,636 on Chainz ↗

Block #2,676,636

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