Block #194,898

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 10:31:57 AM · Difficulty 9.8803 · 6,614,528 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c621792b5a433bd280520f019e391098fd61de92bc6c0013bd7df5bd17a5c29

View on Chainz ↗

Height

#194,898

Difficulty

9.880256

Transactions

Size

617 B

Version

Bits

09e1587d

Nonce

326,514

Timestamp

10/5/2013, 10:31:57 AM

Confirmations

6,614,528

Mined by

⛏️ P2SHAWmrFCSEwMUbRkci4oXi8U653gQAgTUJAp

Merkle Root

47dac98dcb99ce6a6dcf8d1ee61659d1ef5eca32f31b7ed60cce045ecde85aef

Transactions (3)

Coinbasef74e5a5cc9f569…e0d2427e798f8a

1 in → 1 out10.2500 XPM109 B

AWmrFCSE…QAgTUJAp

1803bb9fa0ae90…ad6878a273d56a

1 in → 2 out10.2411 XPM193 B

APbYCiqR…LNsnmyJp AFz9fXym…wh4UqpkL

044623ec1b5fe8…713498e47c2e24

1 in → 2 out6.2073 XPM225 B

AHLqQjYK…4CDrWv66 ASdgjfeT…5rfgZ2Yf

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.

4.754 × 10⁹⁴(95-digit number)

47545118115842981205…31741405144787090399

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

4.754 × 10⁹⁴(95-digit number)

47545118115842981205…31741405144787090399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.754 × 10⁹⁴(95-digit number)

47545118115842981205…31741405144787090401

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

9.509 × 10⁹⁴(95-digit number)

95090236231685962410…63482810289574180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.509 × 10⁹⁴(95-digit number)

95090236231685962410…63482810289574180801

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

1.901 × 10⁹⁵(96-digit number)

19018047246337192482…26965620579148361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.901 × 10⁹⁵(96-digit number)

19018047246337192482…26965620579148361601

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

3.803 × 10⁹⁵(96-digit number)

38036094492674384964…53931241158296723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.803 × 10⁹⁵(96-digit number)

38036094492674384964…53931241158296723201

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

7.607 × 10⁹⁵(96-digit number)

76072188985348769928…07862482316593446399

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 #194,898

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