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Block #2,855,891

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/26/2018, 2:25:28 PM · Difficulty 11.6949 · 3,980,896 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

469f3ffa5735a3326f54370a2937621dd2fdcfe140b97ba1549ae0696759eac7

View on Chainz ↗

Height

#2,855,891

Difficulty

11.694862

Transactions

Size

812 B

Version

Bits

0bb1e27d

Nonce

846,126,441

Timestamp

9/26/2018, 2:25:28 PM

Confirmations

3,980,896

Merkle Root

6357bb84fd7b6d4c4b97c862f6c01c1ca3c893ab3eb374b6770ab49b86ee5a39

Transactions (3)

Coinbaseb59fa2a4741995…a61a37e87846d3

1 in → 1 out7.3200 XPM110 B

AGPuEnfN…2SQ81Wmh

d36bf1c6c3cf06…cffc334028fd17

2 in → 2 out14.5300 XPM305 B

AMDv8zXK…eiALKGNh AZx4Xx9S…ah1QAhSN

ebce15344a3f22…f9bd129adaad83

2 in → 2 out14.5300 XPM306 B

AcXtoaKv…4oXYPT9v AW8FeU4Q…BUVtK3Pq

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.

2.310 × 10⁹⁷(98-digit number)

23104642031720071991…76600366771294123520

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

2.310 × 10⁹⁷(98-digit number)

23104642031720071991…76600366771294123519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.310 × 10⁹⁷(98-digit number)

23104642031720071991…76600366771294123521

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

4.620 × 10⁹⁷(98-digit number)

46209284063440143983…53200733542588247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.620 × 10⁹⁷(98-digit number)

46209284063440143983…53200733542588247041

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

9.241 × 10⁹⁷(98-digit number)

92418568126880287966…06401467085176494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.241 × 10⁹⁷(98-digit number)

92418568126880287966…06401467085176494081

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

1.848 × 10⁹⁸(99-digit number)

18483713625376057593…12802934170352988159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.848 × 10⁹⁸(99-digit number)

18483713625376057593…12802934170352988161

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

3.696 × 10⁹⁸(99-digit number)

36967427250752115186…25605868340705976319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.696 × 10⁹⁸(99-digit number)

36967427250752115186…25605868340705976321

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

7.393 × 10⁹⁸(99-digit number)

73934854501504230373…51211736681411952639

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 2855891

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 469f3ffa5735a3326f54370a2937621dd2fdcfe140b97ba1549ae0696759eac7

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 #2,855,891 on Chainz ↗

Block #2,855,891

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