Block #276,217

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 2:03:05 AM · Difficulty 9.9627 · 6,529,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f73a587b813b9657d1ffa277b9c09f183216c3d782953ba3b222a24d817a91a

View on Chainz ↗

Height

#276,217

Difficulty

9.962652

Transactions

Size

2.80 KB

Version

Bits

09f67063

Nonce

202,700

Timestamp

11/27/2013, 2:03:05 AM

Confirmations

6,529,527

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ac6193c3193057bce722300b9cfd69c40eaf5bb5c434c7b8d739febad9acfffc

Transactions (3)

Coinbase23f26f5aba96f7…b4fce80b3936bb

1 in → 1 out10.0900 XPM110 B

AeKNrjNj…1NEq95Ta

8ed2f78859075f…e6de7104e7b173

4 in → 2 out25.5220 XPM668 B

AY2og4qt…r6CkhngD AaZh6Pi8…bcHSoeth

f4621a8869397e…025c9ae9ef71da

13 in → 2 out4.3581 XPM1.95 KB

Ab1uK9tm…3Xi8tZtX AT1CozhP…VkYVK4BH

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.

2.209 × 10⁹³(94-digit number)

22097231182238232371…94172093299713249279

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

2.209 × 10⁹³(94-digit number)

22097231182238232371…94172093299713249279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.209 × 10⁹³(94-digit number)

22097231182238232371…94172093299713249281

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

4.419 × 10⁹³(94-digit number)

44194462364476464742…88344186599426498559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.419 × 10⁹³(94-digit number)

44194462364476464742…88344186599426498561

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

8.838 × 10⁹³(94-digit number)

88388924728952929485…76688373198852997119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.838 × 10⁹³(94-digit number)

88388924728952929485…76688373198852997121

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

1.767 × 10⁹⁴(95-digit number)

17677784945790585897…53376746397705994239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.767 × 10⁹⁴(95-digit number)

17677784945790585897…53376746397705994241

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

3.535 × 10⁹⁴(95-digit number)

35355569891581171794…06753492795411988479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.535 × 10⁹⁴(95-digit number)

35355569891581171794…06753492795411988481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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