Block #28,366

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 12:02:36 PM · Difficulty 7.9817 · 6,781,415 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c88d7afc774277386ea58f09e38d83b3f6e97a86a07db8374697b2e4aa654790

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Height

#28,366

Difficulty

7.981717

Transactions

Size

199 B

Version

Bits

07fb51cb

Nonce

258

Timestamp

7/13/2013, 12:02:36 PM

Confirmations

6,781,415

Mined by

⛏️ P2SHAWdtCUuJmNjYuej2P6C7RA2SGtHscHZriH

Merkle Root

2aea78c0da87009ae9c265e8d10430f22705cca403a48a7f6a5d789dc41fe694

Transactions (1)

Coinbase2aea78c0da8700…5d789dc41fe694

1 in → 1 out15.6800 XPM109 B

AWdtCUuJ…HscHZriH

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.

6.009 × 10⁹⁵(96-digit number)

60098503521790141075…28159093112229191659

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

6.009 × 10⁹⁵(96-digit number)

60098503521790141075…28159093112229191659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.009 × 10⁹⁵(96-digit number)

60098503521790141075…28159093112229191661

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

1.201 × 10⁹⁶(97-digit number)

12019700704358028215…56318186224458383319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.201 × 10⁹⁶(97-digit number)

12019700704358028215…56318186224458383321

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

2.403 × 10⁹⁶(97-digit number)

24039401408716056430…12636372448916766639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.403 × 10⁹⁶(97-digit number)

24039401408716056430…12636372448916766641

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

4.807 × 10⁹⁶(97-digit number)

48078802817432112860…25272744897833533279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 #28,366

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