Block #276,709

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 7:17:52 AM · Difficulty 9.9640 · 6,517,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

135c76d8398b0eef410cacfbea43a0fa4e3a68aee447b10246c1687a2dc90b42

View on Chainz ↗

Height

#276,709

Difficulty

9.963960

Transactions

Size

1.98 KB

Version

Bits

09f6c614

Nonce

18,255

Timestamp

11/27/2013, 7:17:52 AM

Confirmations

6,517,346

Merkle Root

064f2b716f4c3ec9ac4d618528c433b8be64b715422bc9d06ed5674b2ad7b31a

Transactions (2)

Coinbase0a5514d9206aab…29568f3b0bb9ba

1 in → 31 out10.0400 XPM1.09 KB

AScAzqGc…BZ6tV1vJ AZ2pPuKg…95SN2Yr7 Abv8pzf1…t4zPXDTV ATKK7iFz…wZm46KN1 AFrXbhdx…XkKpGrwu

f29a8093110c20…2b0dad9fb66663

5 in → 2 out57.5600 XPM818 B

AanXnMwV…W8zqECGj ALUr5uUh…mKaVc1PR

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.

2.993 × 10⁹⁰(91-digit number)

29936653945723209236…63005202784364973299

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

2.993 × 10⁹⁰(91-digit number)

29936653945723209236…63005202784364973299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.993 × 10⁹⁰(91-digit number)

29936653945723209236…63005202784364973301

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

5.987 × 10⁹⁰(91-digit number)

59873307891446418473…26010405568729946599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.987 × 10⁹⁰(91-digit number)

59873307891446418473…26010405568729946601

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

1.197 × 10⁹¹(92-digit number)

11974661578289283694…52020811137459893199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.197 × 10⁹¹(92-digit number)

11974661578289283694…52020811137459893201

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

2.394 × 10⁹¹(92-digit number)

23949323156578567389…04041622274919786399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.394 × 10⁹¹(92-digit number)

23949323156578567389…04041622274919786401

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

4.789 × 10⁹¹(92-digit number)

47898646313157134778…08083244549839572799

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