Block #901,207

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2015, 9:38:38 AM · Difficulty 10.9418 · 5,901,567 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

445e76c7ffbeae2e8b0c6ba0dd70bca3064034bc2131d5a11b2543d1ee2aeb66

View on Chainz ↗

Height

#901,207

Difficulty

10.941785

Transactions

Size

903 B

Version

Bits

0af118d2

Nonce

793,162,099

Timestamp

1/19/2015, 9:38:38 AM

Confirmations

5,901,567

Mined by

⛏️ P2SHAYXMenvHkS4yJPvTY6mHSYNffDPHHtybtf

Merkle Root

69ab6a26ed82b80f1bcbdea1b91a313c2ec31a8741a72ef59457cda729bdd438

Transactions (2)

Coinbase5117751e162597…c6e6ee5a729095

1 in → 1 out8.3500 XPM109 B

AYXMenvH…PHHtybtf

0720deeb76fd50…555115c3c3ebbc

4 in → 3 out3923.7647 XPM705 B

AQ5fy2sY…PEW6voxh AGP6xNnA…xrXQAVvd AGuisewS…kixoacNm

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.

2.182 × 10⁹³(94-digit number)

21828263865487092741…97465615755512324179

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

2.182 × 10⁹³(94-digit number)

21828263865487092741…97465615755512324179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.182 × 10⁹³(94-digit number)

21828263865487092741…97465615755512324181

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

4.365 × 10⁹³(94-digit number)

43656527730974185482…94931231511024648359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.365 × 10⁹³(94-digit number)

43656527730974185482…94931231511024648361

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

8.731 × 10⁹³(94-digit number)

87313055461948370965…89862463022049296719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.731 × 10⁹³(94-digit number)

87313055461948370965…89862463022049296721

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

1.746 × 10⁹⁴(95-digit number)

17462611092389674193…79724926044098593439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.746 × 10⁹⁴(95-digit number)

17462611092389674193…79724926044098593441

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

3.492 × 10⁹⁴(95-digit number)

34925222184779348386…59449852088197186879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.492 × 10⁹⁴(95-digit number)

34925222184779348386…59449852088197186881

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