Home/Chain Registry/Block #2,646,048

Block #2,646,048

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 4:28:22 AM · Difficulty 11.7438 · 4,191,274 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

792a6567c4d18e7950a510f00bf3389c0f9dc21cc662f2fa086ffdc78780111c

View on Chainz ↗

Height

#2,646,048

Difficulty

11.743817

Transactions

Size

3.82 KB

Version

Bits

0bbe6ace

Nonce

514,141,438

Timestamp

5/3/2018, 4:28:22 AM

Confirmations

4,191,274

Merkle Root

f61e9e50bc5f2b3a613b2658a5b89226df2371a3cf8b749b73a2455d36b26c5c

Transactions (3)

Coinbase917fbc60d5baa8…b6de898fbacaa9

1 in → 1 out7.3000 XPM110 B

AUDtQwiv…jzNvKJZJ

7a75a6eafc4a92…a642f2ebe86af1

23 in → 2 out492.2305 XPM3.40 KB

AL2EzBxR…kjzAzwzy AeWtf7EL…tEMmpSjw

f48c10eacffc6a…8e7a49ee11e83b

1 in → 2 out11.9900 XPM227 B

AbXqFYdw…z8M9qk6d AJmygDFY…A7mV6JpZ

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.

1.089 × 10⁹⁵(96-digit number)

10899279882723992793…85668906050706394400

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

1.089 × 10⁹⁵(96-digit number)

10899279882723992793…85668906050706394399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.089 × 10⁹⁵(96-digit number)

10899279882723992793…85668906050706394401

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

2.179 × 10⁹⁵(96-digit number)

21798559765447985586…71337812101412788799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.179 × 10⁹⁵(96-digit number)

21798559765447985586…71337812101412788801

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

4.359 × 10⁹⁵(96-digit number)

43597119530895971172…42675624202825577599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.359 × 10⁹⁵(96-digit number)

43597119530895971172…42675624202825577601

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

8.719 × 10⁹⁵(96-digit number)

87194239061791942345…85351248405651155199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.719 × 10⁹⁵(96-digit number)

87194239061791942345…85351248405651155201

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

1.743 × 10⁹⁶(97-digit number)

17438847812358388469…70702496811302310399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.743 × 10⁹⁶(97-digit number)

17438847812358388469…70702496811302310401

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

3.487 × 10⁹⁶(97-digit number)

34877695624716776938…41404993622604620799

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 2646048

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 792a6567c4d18e7950a510f00bf3389c0f9dc21cc662f2fa086ffdc78780111c

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 #2,646,048 on Chainz ↗

Block #2,646,048

Cookie Preferences