Block #276,326

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 3:32:28 AM · Difficulty 9.9629 · 6,566,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aee6fef95ca381c41358ac792a8c8ba3a5fc8b976c00afd2bc498debabef8d65

View on Chainz ↗

Height

#276,326

Difficulty

9.962880

Transactions

Size

936 B

Version

Bits

09f67f4a

Nonce

95,351

Timestamp

11/27/2013, 3:32:28 AM

Confirmations

6,566,258

Mined by

⛏️ f7aRe!ALxZyJxf8kVAeVR1ZGwgmycXcby1f3ARgv

Merkle Root

ec8981325af9869cdca52f901ddc90d6758f27d3a246dcd6aa381c3b42f7f0d1

Transactions (1)

Coinbaseec8981325af986…381c3b42f7f0d1

1 in → 23 out10.0600 XPM845 B

ALxZyJxf…y1f3ARgv APgFFC7i…JbHvBuE9 AVSRHCfX…pYML2Mhc AM38npKs…4sPapue3 AWGQhzDN…RDYvugUy

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.

1.043 × 10⁹⁸(99-digit number)

10437759539077864696…12191896346062700799

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

1.043 × 10⁹⁸(99-digit number)

10437759539077864696…12191896346062700799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.043 × 10⁹⁸(99-digit number)

10437759539077864696…12191896346062700801

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

2.087 × 10⁹⁸(99-digit number)

20875519078155729392…24383792692125401599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.087 × 10⁹⁸(99-digit number)

20875519078155729392…24383792692125401601

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

4.175 × 10⁹⁸(99-digit number)

41751038156311458785…48767585384250803199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.175 × 10⁹⁸(99-digit number)

41751038156311458785…48767585384250803201

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

8.350 × 10⁹⁸(99-digit number)

83502076312622917570…97535170768501606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.350 × 10⁹⁸(99-digit number)

83502076312622917570…97535170768501606401

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

1.670 × 10⁹⁹(100-digit number)

16700415262524583514…95070341537003212799

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 #276,326

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