Block #27,608

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 9:25:53 AM · Difficulty 7.9794 · 6,765,459 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cfa0cca2ffe5ce32eb3d163aec3136d0f947a9505c1bf073019da5f60958a693

View on Chainz ↗

Height

#27,608

Difficulty

7.979381

Transactions

Size

1015 B

Version

Bits

07fab8b5

Nonce

1,077

Timestamp

7/13/2013, 9:25:53 AM

Confirmations

6,765,459

Merkle Root

fb6dee08b35f3931b9d3a2de9384d271f5a49e0a42a680b71511d335997b1f93

Transactions (2)

Coinbase6c668d6d93c5db…70c1a11b7eb435

1 in → 1 out15.7000 XPM108 B

AZm3moqB…xBYCCk2G

0e70eb6406363f…ffe52e73687442

5 in → 2 out157.7878 XPM817 B

ASoqGnYi…MCQqnY9c ALpYif1e…EJ4xJG9q

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.

1.125 × 10⁹⁵(96-digit number)

11250615872849287708…59235259868400504319

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

1.125 × 10⁹⁵(96-digit number)

11250615872849287708…59235259868400504319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.125 × 10⁹⁵(96-digit number)

11250615872849287708…59235259868400504321

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

2.250 × 10⁹⁵(96-digit number)

22501231745698575417…18470519736801008639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.250 × 10⁹⁵(96-digit number)

22501231745698575417…18470519736801008641

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

4.500 × 10⁹⁵(96-digit number)

45002463491397150834…36941039473602017279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.500 × 10⁹⁵(96-digit number)

45002463491397150834…36941039473602017281

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

9.000 × 10⁹⁵(96-digit number)

90004926982794301668…73882078947204034559

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