Block #436,207

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/9/2014, 10:55:22 AM · Difficulty 10.3574 · 6,360,190 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

681ea03e3547f02c786e70247df7b4bb5e95f6a606496edba73c0181acc5e450

View on Chainz ↗

Height

#436,207

Difficulty

10.357419

Transactions

Size

1.40 KB

Version

Bits

0a5b7fcb

Nonce

10,292,130

Timestamp

3/9/2014, 10:55:22 AM

Confirmations

6,360,190

Mined by

⛏️ P2SHAeDP7PSmSaEpjJsCLvK7Vr1G4KBZHSiXHf

Merkle Root

ddad3eeda5d4f8fe5805aa4c8ed3dcb5c2fee5ae9aac3af3f8f18ff91ea967b4

Transactions (2)

Coinbase69d362e6de5056…d5d8370cc43c82

1 in → 1 out9.3300 XPM109 B

AeDP7PSm…BZHSiXHf

3d86374bb8d7ca…6861278b0c244b

6 in → 14 out41.6765 XPM1.21 KB

AboBVJAY…J5wv29PY AeKNrjNj…1NEq95Ta AWpRDakv…F9FTJmL2 ARsimXrf…VdJsFRB6 AdZKGbe9…j9mVS64K

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.

9.434 × 10⁹⁶(97-digit number)

94340179423171734481…98289107466472371199

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

9.434 × 10⁹⁶(97-digit number)

94340179423171734481…98289107466472371199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.434 × 10⁹⁶(97-digit number)

94340179423171734481…98289107466472371201

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

1.886 × 10⁹⁷(98-digit number)

18868035884634346896…96578214932944742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.886 × 10⁹⁷(98-digit number)

18868035884634346896…96578214932944742401

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

3.773 × 10⁹⁷(98-digit number)

37736071769268693792…93156429865889484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.773 × 10⁹⁷(98-digit number)

37736071769268693792…93156429865889484801

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

7.547 × 10⁹⁷(98-digit number)

75472143538537387584…86312859731778969599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.547 × 10⁹⁷(98-digit number)

75472143538537387584…86312859731778969601

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

1.509 × 10⁹⁸(99-digit number)

15094428707707477516…72625719463557939199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.509 × 10⁹⁸(99-digit number)

15094428707707477516…72625719463557939201

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.018 × 10⁹⁸(99-digit number)

30188857415414955033…45251438927115878399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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