Block #1,231,540

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2015, 9:06:33 AM · Difficulty 10.7388 · 5,581,296 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5e8b8891fee5b4d9b280194270996ee7ccbb2261fd5ccf5e2bda801e4d6dbab

View on Chainz ↗

Height

#1,231,540

Difficulty

10.738779

Transactions

Size

5.88 KB

Version

Bits

0abd20a7

Nonce

277,945,091

Timestamp

9/11/2015, 9:06:33 AM

Confirmations

5,581,296

Mined by

⛏️ P2SHAYB6MrvEVeQxNpmay17N8u1ouyQm9BzM9X

Merkle Root

2f65fa5689a96e84c8d8e9af0f4a76146584cbbcfc7fdbf84db193c6421d2d55

Transactions (4)

Coinbase573a8506eecb5b…34177d64cde6b7

1 in → 1 out8.7300 XPM110 B

AYB6MrvE…Qm9BzM9X

0f387c9df6ea42…029be5faa3ce1f

1 in → 51 out22.6503 XPM1.85 KB

AaR2V7mf…5pES65VG ATkiCeum…91r8eHmY AYAk96xm…MDv3UkUs AUhLZdsR…gKMfjeDb Adn6K5UG…3gkw6BeU

df63e55bd410a2…2f3e2ac2526495

2 in → 51 out1.3548 XPM1.99 KB

AJtr6R7n…gwiPT1ev AX6oJXsR…NsFeV4Bn AcBbo6oY…jWnxn7uY AR97W6eb…5zP5btwY Ac3MQYnX…Xt5VQHvD

e22f4e10bf99a0…cd15d0be05ddd6

1 in → 51 out1.9900 XPM1.85 KB

AYZ3QdHR…k32aGFvf AS5G2LFg…rr4LZQzk AXu4rsPT…opKXv1ch ANRoFQYh…us3JahGc AMtRyMNz…rahnfSa4

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.

3.872 × 10⁹⁷(98-digit number)

38725493204660658411…02654250650603519999

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

3.872 × 10⁹⁷(98-digit number)

38725493204660658411…02654250650603519999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.872 × 10⁹⁷(98-digit number)

38725493204660658411…02654250650603520001

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

7.745 × 10⁹⁷(98-digit number)

77450986409321316823…05308501301207039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.745 × 10⁹⁷(98-digit number)

77450986409321316823…05308501301207040001

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

1.549 × 10⁹⁸(99-digit number)

15490197281864263364…10617002602414079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.549 × 10⁹⁸(99-digit number)

15490197281864263364…10617002602414080001

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

3.098 × 10⁹⁸(99-digit number)

30980394563728526729…21234005204828159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.098 × 10⁹⁸(99-digit number)

30980394563728526729…21234005204828160001

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

6.196 × 10⁹⁸(99-digit number)

61960789127457053458…42468010409656319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.196 × 10⁹⁸(99-digit number)

61960789127457053458…42468010409656320001

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 #1,231,540

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