Block #1,141,405

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/5/2015, 11:06:35 PM · Difficulty 10.9322 · 5,685,561 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b8fd97aebfbc9baa001dfd524e7293e4b2383533613701d8bed9e218ff8658a

View on Chainz ↗

Height

#1,141,405

Difficulty

10.932189

Transactions

Size

4.32 KB

Version

Bits

0aeea3ed

Nonce

1,616,593,306

Timestamp

7/5/2015, 11:06:35 PM

Confirmations

5,685,561

Mined by

⛏️ P2SHARPgjMux3NCrbP51LT8jmSNQXLz1JqNE4A

Merkle Root

e97a48c1b4bd480288354f97663b6b0e3a584624e80232d3b807aa64616d6fcf

Transactions (3)

Coinbasebfd4f07f918914…540530da99d95f

1 in → 1 out8.4000 XPM110 B

ARPgjMux…z1JqNE4A

3e7ab6bb69d89e…8f7fc69bbdf1e9

1 in → 51 out78.3309 XPM1.85 KB

AU4f4km9…u8UnNcJ8 ATkiCeum…91r8eHmY AJab5pQJ…NDncq51r AJjBEWkV…NaX1dQm4 AXoirxXr…s3xo7iCx

b30e9f515b913b…0b68702f717faf

4 in → 51 out0.6966 XPM2.28 KB

ANZS73Sv…Na4ACxq8 AStLQwmr…QSUwG9HE AbFWECxS…Zmp2qruU AGwbxzZC…qRzQdmue AKJTDxwW…HcrWTrPn

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.

6.369 × 10⁹⁵(96-digit number)

63699191525307284541…01913983644168854719

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

6.369 × 10⁹⁵(96-digit number)

63699191525307284541…01913983644168854719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.369 × 10⁹⁵(96-digit number)

63699191525307284541…01913983644168854721

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

1.273 × 10⁹⁶(97-digit number)

12739838305061456908…03827967288337709439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.273 × 10⁹⁶(97-digit number)

12739838305061456908…03827967288337709441

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

2.547 × 10⁹⁶(97-digit number)

25479676610122913816…07655934576675418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.547 × 10⁹⁶(97-digit number)

25479676610122913816…07655934576675418881

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

5.095 × 10⁹⁶(97-digit number)

50959353220245827633…15311869153350837759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.095 × 10⁹⁶(97-digit number)

50959353220245827633…15311869153350837761

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

1.019 × 10⁹⁷(98-digit number)

10191870644049165526…30623738306701675519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.019 × 10⁹⁷(98-digit number)

10191870644049165526…30623738306701675521

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 #1,141,405

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