Block #207,832

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 4:14:51 PM · Difficulty 9.9041 · 6,608,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6a82d24e31d828db06418ba4b42c86ccbf3329b3b9de2218e5b22a5752d0522

View on Chainz ↗

Height

#207,832

Difficulty

9.904146

Transactions

Size

4.10 KB

Version

Bits

09e7761a

Nonce

1,165,038,371

Timestamp

10/13/2013, 4:14:51 PM

Confirmations

6,608,610

Mined by

⛏️ +RZAGYGiNnKhiPBKAPeJ2uayETKMUcSKYNi1g

Merkle Root

2b7c831a709c4fac145d61858d2c7c5672dc8e7389d99dbb5a3b5631514ec168

Transactions (1)

Coinbase2b7c831a709c4f…3b5631514ec168

1 in → 119 out10.1300 XPM4.01 KB

AGYGiNnK…cSKYNi1g AZg7roHp…YqFP96Sd ANfpVCC4…Qu8GmRLT AWRwRUpA…n62qYTQS ANKaqdoT…rPahfJui

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.

1.182 × 10⁹⁵(96-digit number)

11827670289470393170…51066869758856861199

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

1.182 × 10⁹⁵(96-digit number)

11827670289470393170…51066869758856861199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.182 × 10⁹⁵(96-digit number)

11827670289470393170…51066869758856861201

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

2.365 × 10⁹⁵(96-digit number)

23655340578940786340…02133739517713722399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.365 × 10⁹⁵(96-digit number)

23655340578940786340…02133739517713722401

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

4.731 × 10⁹⁵(96-digit number)

47310681157881572680…04267479035427444799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.731 × 10⁹⁵(96-digit number)

47310681157881572680…04267479035427444801

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

9.462 × 10⁹⁵(96-digit number)

94621362315763145361…08534958070854889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.462 × 10⁹⁵(96-digit number)

94621362315763145361…08534958070854889601

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

1.892 × 10⁹⁶(97-digit number)

18924272463152629072…17069916141709779199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #207,832

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