Block #1,332,555

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/18/2015, 10:05:23 PM · Difficulty 10.8381 · 5,494,558 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

912283b141df5f13f3c960f507f4088840e1e5a6dd64adceb197ff4f916c5860

View on Chainz ↗

Height

#1,332,555

Difficulty

10.838138

Transactions

Size

1.28 KB

Version

Bits

0ad69036

Nonce

47,761,510

Timestamp

11/18/2015, 10:05:23 PM

Confirmations

5,494,558

Mined by

⛏️ P2SHAP6dxKTgdW4yqEB5c6sTR9EWC6TqTnFqFs

Merkle Root

c4d82c793ddcab93f7510d0b5b4f1060e792cfebc707188c0d3ef6eea90d39a4

Transactions (2)

Coinbase89c0f1d492c627…b406e85a31d469

1 in → 1 out8.5200 XPM110 B

AP6dxKTg…TqTnFqFs

a43d07ff29b159…5810abc5b9a8c8

1 in → 28 out139.5441 XPM1.08 KB

AG97kpGV…BGGHr9WA APmsuvgi…rc3Qe2d7 ATMCrZhw…GnzPhunm Acjcbpe7…3ZfTEWmo ARupRzGn…FYjvXdLM

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.

6.613 × 10⁹⁶(97-digit number)

66138194070093607492…58475591228441313279

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

6.613 × 10⁹⁶(97-digit number)

66138194070093607492…58475591228441313279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.613 × 10⁹⁶(97-digit number)

66138194070093607492…58475591228441313281

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

1.322 × 10⁹⁷(98-digit number)

13227638814018721498…16951182456882626559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.322 × 10⁹⁷(98-digit number)

13227638814018721498…16951182456882626561

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

2.645 × 10⁹⁷(98-digit number)

26455277628037442996…33902364913765253119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.645 × 10⁹⁷(98-digit number)

26455277628037442996…33902364913765253121

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

5.291 × 10⁹⁷(98-digit number)

52910555256074885993…67804729827530506239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.291 × 10⁹⁷(98-digit number)

52910555256074885993…67804729827530506241

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

1.058 × 10⁹⁸(99-digit number)

10582111051214977198…35609459655061012479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.058 × 10⁹⁸(99-digit number)

10582111051214977198…35609459655061012481

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 #1,332,555

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