Home/Chain Registry/Block #2,636,307

Block #2,636,307

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 1:05:58 PM · Difficulty 11.3740 · 4,194,275 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0afb7351240c68fc7019fd91a2a71ab2c778b47ac23899f6fa92e4fadf9130eb

View on Chainz ↗

Height

#2,636,307

Difficulty

11.374050

Transactions

Size

1.07 KB

Version

Bits

0b5fc1ba

Nonce

2,067,052,586

Timestamp

4/29/2018, 1:05:58 PM

Confirmations

4,194,275

Merkle Root

761b30a1083c6a9cb8a3762c6f54479abf3734130486a6d8712f800f11de2496

Transactions (3)

Coinbaseb40439277bb017…44b6ed4d7a63ac

1 in → 1 out7.7400 XPM110 B

Adqah8zh…1WwoHJ9t

e1308c814aa00b…6fdf15f6c3f96f

2 in → 2 out11.2503 XPM374 B

AX34uEPT…2bFAXZMk AWQrJyH2…RbvihCDK

7000266f44edc4…4ece5d296e3f5f

3 in → 2 out6.1253 XPM525 B

AGHPVXdJ…ZkUDM8fN AdWNahYS…codohPEh

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.

1.505 × 10⁹³(94-digit number)

15058434978459732814…84485081139426519840

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

1.505 × 10⁹³(94-digit number)

15058434978459732814…84485081139426519839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.505 × 10⁹³(94-digit number)

15058434978459732814…84485081139426519841

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

3.011 × 10⁹³(94-digit number)

30116869956919465629…68970162278853039679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.011 × 10⁹³(94-digit number)

30116869956919465629…68970162278853039681

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

6.023 × 10⁹³(94-digit number)

60233739913838931258…37940324557706079359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.023 × 10⁹³(94-digit number)

60233739913838931258…37940324557706079361

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

1.204 × 10⁹⁴(95-digit number)

12046747982767786251…75880649115412158719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.204 × 10⁹⁴(95-digit number)

12046747982767786251…75880649115412158721

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

2.409 × 10⁹⁴(95-digit number)

24093495965535572503…51761298230824317439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.409 × 10⁹⁴(95-digit number)

24093495965535572503…51761298230824317441

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

4.818 × 10⁹⁴(95-digit number)

48186991931071145006…03522596461648634879

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 2636307

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 0afb7351240c68fc7019fd91a2a71ab2c778b47ac23899f6fa92e4fadf9130eb

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 #2,636,307 on Chainz ↗

Block #2,636,307

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