Block #436,384

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 1:43:36 PM · Difficulty 10.3586 · 6,355,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

34f3fbd6f01f7b3d963d6426f8ff86344c141d90de8810b67e2f707bf16838f4

View on Chainz ↗

Height

#436,384

Difficulty

10.358636

Transactions

Size

8.80 KB

Version

Bits

0a5bcf90

Nonce

19,450

Timestamp

3/9/2014, 1:43:36 PM

Confirmations

6,355,167

Merkle Root

778a915f6e35b4a7dcd8b2c383b267a8a1b08c6b49b4eebb6560609991bb0ffe

Transactions (2)

Coinbasecfee045fff3fb1…4e3bb5a6aafba0

1 in → 1 out9.5300 XPM110 B

AeKNrjNj…1NEq95Ta

568fcd4fdeb894…aee90d1f39bb4a

59 in → 2 out10000.0100 XPM8.60 KB

Ae5WFHbn…gBo7rvHr AXkWMYim…F2EYm97d

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.

2.294 × 10⁹⁵(96-digit number)

22946477154524752023…59783600919506785279

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

2.294 × 10⁹⁵(96-digit number)

22946477154524752023…59783600919506785279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.294 × 10⁹⁵(96-digit number)

22946477154524752023…59783600919506785281

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

4.589 × 10⁹⁵(96-digit number)

45892954309049504046…19567201839013570559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.589 × 10⁹⁵(96-digit number)

45892954309049504046…19567201839013570561

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

9.178 × 10⁹⁵(96-digit number)

91785908618099008092…39134403678027141119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.178 × 10⁹⁵(96-digit number)

91785908618099008092…39134403678027141121

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

1.835 × 10⁹⁶(97-digit number)

18357181723619801618…78268807356054282239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.835 × 10⁹⁶(97-digit number)

18357181723619801618…78268807356054282241

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

3.671 × 10⁹⁶(97-digit number)

36714363447239603237…56537614712108564479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.671 × 10⁹⁶(97-digit number)

36714363447239603237…56537614712108564481

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