Block #1,366,431

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2015, 8:08:58 AM · Difficulty 10.8443 · 5,450,535 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce014b9ac98094c6dc5351c2fab35844678b828927bd0868bd64fc2328e1a576

View on Chainz ↗

Height

#1,366,431

Difficulty

10.844320

Transactions

Size

834 B

Version

Bits

0ad82563

Nonce

158,716,075

Timestamp

12/12/2015, 8:08:58 AM

Confirmations

5,450,535

Mined by

⛏️ P2SHAWfz2yZh28tCJSGu4pffcMVbK7YFpVCPfs

Merkle Root

10976bc6da5a129048524f5982c315de867c3b748987757558efa4abb90d0091

Transactions (2)

Coinbase6c114fdc400f6a…0a7bc8a983a754

1 in → 1 out8.5000 XPM110 B

AWfz2yZh…YFpVCPfs

c21bbccfda9de3…aae5f29800d544

1 in → 14 out103.3253 XPM633 B

AcZ2w3NH…5avstJwr Ac2mpfHM…RYztA5d8 AR4VVnHW…MTajNsvq AXLkjH6Q…9wXKhR9V ATyHFdjS…kku74cEm

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.

1.486 × 10⁹⁶(97-digit number)

14865358702859916775…92491994620419059199

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

1.486 × 10⁹⁶(97-digit number)

14865358702859916775…92491994620419059199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.486 × 10⁹⁶(97-digit number)

14865358702859916775…92491994620419059201

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

2.973 × 10⁹⁶(97-digit number)

29730717405719833551…84983989240838118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.973 × 10⁹⁶(97-digit number)

29730717405719833551…84983989240838118401

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

5.946 × 10⁹⁶(97-digit number)

59461434811439667103…69967978481676236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.946 × 10⁹⁶(97-digit number)

59461434811439667103…69967978481676236801

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

1.189 × 10⁹⁷(98-digit number)

11892286962287933420…39935956963352473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.189 × 10⁹⁷(98-digit number)

11892286962287933420…39935956963352473601

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

2.378 × 10⁹⁷(98-digit number)

23784573924575866841…79871913926704947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.378 × 10⁹⁷(98-digit number)

23784573924575866841…79871913926704947201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,366,431

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