Block #1,267,900

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/5/2015, 8:44:15 AM · Difficulty 10.8191 · 5,542,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36b9a08522fcae4bcf7121c4d48d0d32c1203ff91c44a1c525b28343716fe226

View on Chainz ↗

Height

#1,267,900

Difficulty

10.819055

Transactions

Size

29.17 KB

Version

Bits

0ad1ad9d

Nonce

645,440,893

Timestamp

10/5/2015, 8:44:15 AM

Confirmations

5,542,167

Mined by

⛏️ P2SHAchKYZFbe9K2fYEErVqYbrdtLQJsfBeN4u

Merkle Root

a32c31f136db5f88db5292de95c2aec95528335d36f7beba393140a946952209

Transactions (2)

Coinbase507e557e669587…edc1f28af01169

1 in → 1 out8.8500 XPM110 B

AchKYZFb…JsfBeN4u

e0a537d87b323c…1f6e00aa745cb7

200 in → 2 out1066.0421 XPM28.97 KB

AM51fttS…Ztf8prfj AQ8obrRF…hCezsXdr

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.

6.349 × 10⁹³(94-digit number)

63495644182266473109…19886040362935409919

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

6.349 × 10⁹³(94-digit number)

63495644182266473109…19886040362935409919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.349 × 10⁹³(94-digit number)

63495644182266473109…19886040362935409921

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

1.269 × 10⁹⁴(95-digit number)

12699128836453294621…39772080725870819839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.269 × 10⁹⁴(95-digit number)

12699128836453294621…39772080725870819841

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

2.539 × 10⁹⁴(95-digit number)

25398257672906589243…79544161451741639679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.539 × 10⁹⁴(95-digit number)

25398257672906589243…79544161451741639681

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

5.079 × 10⁹⁴(95-digit number)

50796515345813178487…59088322903483279359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.079 × 10⁹⁴(95-digit number)

50796515345813178487…59088322903483279361

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

1.015 × 10⁹⁵(96-digit number)

10159303069162635697…18176645806966558719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.015 × 10⁹⁵(96-digit number)

10159303069162635697…18176645806966558721

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 #1,267,900

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