Block #2,936,643

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/24/2018, 3:16:51 AM · Difficulty 11.3887 · 3,897,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

760eae8017ca6cea180ae4f6ef1d22b383a1e5feca18165a30124fc257ffeb62

View on Chainz ↗

Height

#2,936,643

Difficulty

11.388723

Transactions

Size

610 B

Version

Bits

0b638352

Nonce

105,071,103

Timestamp

11/24/2018, 3:16:51 AM

Confirmations

3,897,212

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

2d3cea467d06d2510281b03149037ef7b304a14567c9ca1cf81d4816373c7a21

Transactions (2)

Coinbase97c9d56dce2fb4…c505ee82b12943

1 in → 1 out7.7100 XPM110 B

AUhjokok…k5m93PZR

dbbc2ee430d0f9…4629cb21a2740d

2 in → 3 out262.3414 XPM408 B

AQKz6Qpg…r7zmnHmK AJgMrEpx…feT4viBK Ac7Navjw…VbfnsbSj

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.

2.430 × 10⁹⁸(99-digit number)

24304346512029506626…08172398798704639999

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

2.430 × 10⁹⁸(99-digit number)

24304346512029506626…08172398798704639999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.430 × 10⁹⁸(99-digit number)

24304346512029506626…08172398798704640001

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

4.860 × 10⁹⁸(99-digit number)

48608693024059013252…16344797597409279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.860 × 10⁹⁸(99-digit number)

48608693024059013252…16344797597409280001

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

9.721 × 10⁹⁸(99-digit number)

97217386048118026505…32689595194818559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.721 × 10⁹⁸(99-digit number)

97217386048118026505…32689595194818560001

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

1.944 × 10⁹⁹(100-digit number)

19443477209623605301…65379190389637119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.944 × 10⁹⁹(100-digit number)

19443477209623605301…65379190389637120001

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

3.888 × 10⁹⁹(100-digit number)

38886954419247210602…30758380779274239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.888 × 10⁹⁹(100-digit number)

38886954419247210602…30758380779274240001

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

7.777 × 10⁹⁹(100-digit number)

77773908838494421204…61516761558548479999

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.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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

Cross-reference on Chainz Explorer

Block #2,936,643

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