Block #191,877

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 11:14:35 AM · Difficulty 9.8753 · 6,616,125 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5777b39aa74a4c47e91008c97b06a8b7bbe66ffd739412e566c6041b15dd0a4c

View on Chainz ↗

Height

#191,877

Difficulty

9.875272

Transactions

Size

542 B

Version

Bits

09e011cd

Nonce

115,186

Timestamp

10/3/2013, 11:14:35 AM

Confirmations

6,616,125

Mined by

⛏️ P2SHAXtUHczob3NNdpiGvxAE1JUJfgKe72YFw4

Merkle Root

dfacf81cbda65c6a4a377bab9e77818251572a9a550f258cb78acb44c9244e54

Transactions (2)

Coinbasedcdac91138b589…6f69a7a84dedd2

1 in → 1 out10.2500 XPM110 B

AXtUHczo…Ke72YFw4

49f7f3dbedadfe…f7bf543ef80782

2 in → 1 out30.7600 XPM341 B

AbEVNHvT…4XP8UPJZ

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.

1.333 × 10⁹⁷(98-digit number)

13331683032514715204…92460493197700638599

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

1.333 × 10⁹⁷(98-digit number)

13331683032514715204…92460493197700638599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.333 × 10⁹⁷(98-digit number)

13331683032514715204…92460493197700638601

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

2.666 × 10⁹⁷(98-digit number)

26663366065029430408…84920986395401277199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.666 × 10⁹⁷(98-digit number)

26663366065029430408…84920986395401277201

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

5.332 × 10⁹⁷(98-digit number)

53326732130058860817…69841972790802554399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.332 × 10⁹⁷(98-digit number)

53326732130058860817…69841972790802554401

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

1.066 × 10⁹⁸(99-digit number)

10665346426011772163…39683945581605108799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.066 × 10⁹⁸(99-digit number)

10665346426011772163…39683945581605108801

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

2.133 × 10⁹⁸(99-digit number)

21330692852023544327…79367891163210217599

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 #191,877

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