Block #199,463

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 9:44:56 AM · Difficulty 9.8874 · 6,596,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa047c71af6ba15b583d4f60dbbe6e85482fe685d896ba70de9846d13df485c4

View on Chainz ↗

Height

#199,463

Difficulty

9.887410

Transactions

Size

1.08 KB

Version

Bits

09e32d4e

Nonce

4,694

Timestamp

10/8/2013, 9:44:56 AM

Confirmations

6,596,745

Mined by

⛏️ P2SHAchLk8L8RhQ9PmqnyDdQ3d7WmjiYwuz8y8

Merkle Root

2df4e161d10037f2c1bc9b8d9415021cde22b923f081639d6f668144ede09965

Transactions (5)

Coinbase68d6d74bbde30e…9bf30d4c5c24dc

1 in → 1 out10.2500 XPM109 B

AchLk8L8…iYwuz8y8

5076a74711a4c5…adee6dc853f0f5

1 in → 2 out10.2200 XPM226 B

AVTssqMN…ajDfdPmP AMFNEmnP…oj9wiV7V

249773476ba557…5230dca21021b4

1 in → 2 out37.8400 XPM225 B

AbHMdF6f…C6T8emhS ASUJFtQT…Cqr8nBVx

757fa82feaaee2…f3f996aa6945f5

1 in → 2 out4.1554 XPM226 B

AVRZQJDK…RRRxzW2J AaxyHNzV…DsMMnaW1

b7068174c52c75…74a9ebbc8aa183

1 in → 2 out0.6900 XPM226 B

AWCthphG…BBD9x6vx ASUJFtQT…Cqr8nBVx

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.

2.517 × 10⁹³(94-digit number)

25173081022584699173…34647085653231683029

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

2.517 × 10⁹³(94-digit number)

25173081022584699173…34647085653231683029

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.517 × 10⁹³(94-digit number)

25173081022584699173…34647085653231683031

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

5.034 × 10⁹³(94-digit number)

50346162045169398346…69294171306463366059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.034 × 10⁹³(94-digit number)

50346162045169398346…69294171306463366061

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

1.006 × 10⁹⁴(95-digit number)

10069232409033879669…38588342612926732119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.006 × 10⁹⁴(95-digit number)

10069232409033879669…38588342612926732121

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

2.013 × 10⁹⁴(95-digit number)

20138464818067759338…77176685225853464239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.013 × 10⁹⁴(95-digit number)

20138464818067759338…77176685225853464241

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

4.027 × 10⁹⁴(95-digit number)

40276929636135518677…54353370451706928479

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