Block #198,481

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/7/2013, 6:31:45 PM · Difficulty 9.8859 · 6,628,439 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d32209b0dfcc46528c4332cb40deb8b7b5d8053d5d8daec6d354f53f6e879fea

View on Chainz ↗

Height

#198,481

Difficulty

9.885878

Transactions

Size

423 B

Version

Bits

09e2c8df

Nonce

144,126

Timestamp

10/7/2013, 6:31:45 PM

Confirmations

6,628,439

Mined by

⛏️ P2SHAKDazacJDW3kSrN6AqgUTN8hg73JrszznZ

Merkle Root

3fb9f906e0fc1297b6d46b5fadc239e11a087b3211ef824110489d61c0f4ca85

Transactions (2)

Coinbaseeae90d620f3a6c…c96e986d00ea15

1 in → 1 out10.2300 XPM109 B

AKDazacJ…3JrszznZ

06e1d9b3879878…4273e7fa8b19af

1 in → 2 out3.1408 XPM225 B

AdD8Vo1u…EFD5dqoQ AMZyS2P8…cqcMgvRe

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.

1.589 × 10⁹³(94-digit number)

15896740054771058526…14570098905356369139

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

1.589 × 10⁹³(94-digit number)

15896740054771058526…14570098905356369139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.589 × 10⁹³(94-digit number)

15896740054771058526…14570098905356369141

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

3.179 × 10⁹³(94-digit number)

31793480109542117052…29140197810712738279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.179 × 10⁹³(94-digit number)

31793480109542117052…29140197810712738281

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

6.358 × 10⁹³(94-digit number)

63586960219084234104…58280395621425476559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.358 × 10⁹³(94-digit number)

63586960219084234104…58280395621425476561

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

1.271 × 10⁹⁴(95-digit number)

12717392043816846820…16560791242850953119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.271 × 10⁹⁴(95-digit number)

12717392043816846820…16560791242850953121

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

2.543 × 10⁹⁴(95-digit number)

25434784087633693641…33121582485701906239

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 #198,481

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