Block #275,629

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 7:15:27 PM · Difficulty 9.9613 · 6,549,152 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

818e5c11172c850b8ae9b18bf5af0374b692d381f7e2e91dd3000bb524b7ff93

View on Chainz ↗

Height

#275,629

Difficulty

9.961266

Transactions

Size

1.63 KB

Version

Bits

09f61586

Nonce

17,312

Timestamp

11/26/2013, 7:15:27 PM

Confirmations

6,549,152

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

58cad7cbce62c2d1e8fbb7c92de60303ff193f5c42cc3fe9a32070a7f799e0d4

Transactions (4)

Coinbase6b6421455fc1fb…bf424efff4b884

1 in → 1 out10.1000 XPM110 B

AeKNrjNj…1NEq95Ta

b924db9d8756dc…b262b657cf3dfb

7 in → 1 out47.9892 XPM1.06 KB

ARdkuRAM…6sVtoKTb

c51b4ac96f0ad4…bc3125136a2f00

1 in → 1 out10.0600 XPM159 B

AHXaDpj5…wA4V6fNL

e3ba73712c3051…ab8ee3d90d5b5b

1 in → 3 out10.0800 XPM227 B

ASsZ8gkf…EvjaZhvT AeKNrjNj…1NEq95Ta ATYwNvuN…t2K91Utn

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.

4.856 × 10⁹⁵(96-digit number)

48560624236649431885…67393172282162534399

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

4.856 × 10⁹⁵(96-digit number)

48560624236649431885…67393172282162534399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.856 × 10⁹⁵(96-digit number)

48560624236649431885…67393172282162534401

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

9.712 × 10⁹⁵(96-digit number)

97121248473298863771…34786344564325068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.712 × 10⁹⁵(96-digit number)

97121248473298863771…34786344564325068801

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

1.942 × 10⁹⁶(97-digit number)

19424249694659772754…69572689128650137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.942 × 10⁹⁶(97-digit number)

19424249694659772754…69572689128650137601

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

3.884 × 10⁹⁶(97-digit number)

38848499389319545508…39145378257300275199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.884 × 10⁹⁶(97-digit number)

38848499389319545508…39145378257300275201

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

7.769 × 10⁹⁶(97-digit number)

77696998778639091017…78290756514600550399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.769 × 10⁹⁶(97-digit number)

77696998778639091017…78290756514600550401

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

Block #275,629

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