Block #1,311,039

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/3/2015, 5:10:07 PM · Difficulty 10.8492 · 5,513,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

643618d9c3f6df7f4cf907df27a0cc2ed7e121ecf5dd2db6bad5379e6a6ab6ce

View on Chainz ↗

Height

#1,311,039

Difficulty

10.849181

Transactions

Size

1.68 KB

Version

Bits

0ad963eb

Nonce

523,116,809

Timestamp

11/3/2015, 5:10:07 PM

Confirmations

5,513,550

Mined by

⛏️ P2SHASdquGP7MJayYASRqgPXa3qVxnCMinBJAn

Merkle Root

d2ceaa4ad491ec89d89e160690463561b54c0ea0c6febb14b302e0cdd756b4fb

Transactions (2)

Coinbased52108815038d6…8b9916c8d50918

1 in → 1 out8.5000 XPM110 B

ASdquGP7…CMinBJAn

4260bf05ba918e…43cbf9b6249cba

4 in → 27 out0.2981 XPM1.49 KB

AVit2CQs…AcZXuef1 AUCYbvRY…kGc9gFDg APid5Gym…xCUaYTgy AcrHAHCB…d368Uqxw ASK3B1Ax…1nT5ahZN

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.

6.244 × 10⁹⁶(97-digit number)

62442602901045442551…60178115393632911359

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

6.244 × 10⁹⁶(97-digit number)

62442602901045442551…60178115393632911359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.244 × 10⁹⁶(97-digit number)

62442602901045442551…60178115393632911361

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

1.248 × 10⁹⁷(98-digit number)

12488520580209088510…20356230787265822719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.248 × 10⁹⁷(98-digit number)

12488520580209088510…20356230787265822721

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

2.497 × 10⁹⁷(98-digit number)

24977041160418177020…40712461574531645439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.497 × 10⁹⁷(98-digit number)

24977041160418177020…40712461574531645441

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

4.995 × 10⁹⁷(98-digit number)

49954082320836354041…81424923149063290879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.995 × 10⁹⁷(98-digit number)

49954082320836354041…81424923149063290881

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

9.990 × 10⁹⁷(98-digit number)

99908164641672708082…62849846298126581759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.990 × 10⁹⁷(98-digit number)

99908164641672708082…62849846298126581761

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

1.998 × 10⁹⁸(99-digit number)

19981632928334541616…25699692596253163519

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 #1,311,039

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