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Block #2,948,575

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/2/2018, 8:49:12 AM · Difficulty 11.3987 · 3,884,234 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2d62b859fe05e91568b6f0fc5e787718721b8d7191de3e3226bf6b4b69b1c41

View on Chainz ↗

Height

#2,948,575

Difficulty

11.398723

Transactions

Size

1.23 KB

Version

Bits

0b6612ae

Nonce

174,401,372

Timestamp

12/2/2018, 8:49:12 AM

Confirmations

3,884,234

Merkle Root

55175f392f422371dd3312c1d3078278172d318b85b8fa01161144d8d1e98ae5

Transactions (2)

Coinbase95cc20874a6eff…f4e40f5dfa90e3

1 in → 1 out7.7000 XPM110 B

AbXwmGxD…4XXYP765

f6936625b30212…7c06c3cafeb433

8 in → 2 out50.0354 XPM1.03 KB

AJktnhjX…XNqNLjQX 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.

1.318 × 10⁹⁵(96-digit number)

13186818019411108850…30010959347475415040

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

1.318 × 10⁹⁵(96-digit number)

13186818019411108850…30010959347475415039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.318 × 10⁹⁵(96-digit number)

13186818019411108850…30010959347475415041

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

2.637 × 10⁹⁵(96-digit number)

26373636038822217700…60021918694950830079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.637 × 10⁹⁵(96-digit number)

26373636038822217700…60021918694950830081

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

5.274 × 10⁹⁵(96-digit number)

52747272077644435401…20043837389901660159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.274 × 10⁹⁵(96-digit number)

52747272077644435401…20043837389901660161

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

1.054 × 10⁹⁶(97-digit number)

10549454415528887080…40087674779803320319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.054 × 10⁹⁶(97-digit number)

10549454415528887080…40087674779803320321

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

2.109 × 10⁹⁶(97-digit number)

21098908831057774160…80175349559606640639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.109 × 10⁹⁶(97-digit number)

21098908831057774160…80175349559606640641

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

4.219 × 10⁹⁶(97-digit number)

42197817662115548321…60350699119213281279

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 2948575

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 b2d62b859fe05e91568b6f0fc5e787718721b8d7191de3e3226bf6b4b69b1c41

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 #2,948,575 on Chainz ↗

Block #2,948,575

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