Block #1,813,727

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/19/2016, 10:14:28 AM · Difficulty 10.7775 · 5,029,539 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c026eab174b045dc7fc7c5c5520689a96dfb47713ee05f3348687ee7d5e867c3

View on Chainz ↗

Height

#1,813,727

Difficulty

10.777457

Transactions

Size

1.97 KB

Version

Bits

0ac7076d

Nonce

1,960,771,376

Timestamp

10/19/2016, 10:14:28 AM

Confirmations

5,029,539

Mined by

⛏️ P2SHATj43CBmzNDxdgWDRJX5tXU9HozFaUuCti

Merkle Root

baaddb0f8a4ff4030177450dd59cc6ee8d365380dc381d755afc8f4f089dedb3

Transactions (2)

Coinbaseea5587c2790067…3a1f8e36cf30f7

1 in → 1 out8.6200 XPM109 B

ATj43CBm…zFaUuCti

9b652dd6b19f07…1de961a240ae3c

12 in → 1 out51.9800 XPM1.77 KB

AVtWEnxx…nytVBavj

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.

6.225 × 10⁹⁵(96-digit number)

62255834380664055125…67153041185572126719

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

6.225 × 10⁹⁵(96-digit number)

62255834380664055125…67153041185572126719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.225 × 10⁹⁵(96-digit number)

62255834380664055125…67153041185572126721

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

1.245 × 10⁹⁶(97-digit number)

12451166876132811025…34306082371144253439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.245 × 10⁹⁶(97-digit number)

12451166876132811025…34306082371144253441

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

2.490 × 10⁹⁶(97-digit number)

24902333752265622050…68612164742288506879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.490 × 10⁹⁶(97-digit number)

24902333752265622050…68612164742288506881

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

4.980 × 10⁹⁶(97-digit number)

49804667504531244100…37224329484577013759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.980 × 10⁹⁶(97-digit number)

49804667504531244100…37224329484577013761

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

9.960 × 10⁹⁶(97-digit number)

99609335009062488200…74448658969154027519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.960 × 10⁹⁶(97-digit number)

99609335009062488200…74448658969154027521

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 #1,813,727

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