Block #432,044

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 2:56:12 PM · Difficulty 10.3443 · 6,384,940 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc1824262017b0fb0fdae04506a316ff8e222c9da566a80aab3450f1ce15acb6

View on Chainz ↗

Height

#432,044

Difficulty

10.344294

Transactions

Size

1.91 KB

Version

Bits

0a5823a3

Nonce

182,675

Timestamp

3/6/2014, 2:56:12 PM

Confirmations

6,384,940

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

2afc6bca05f0310b6ca0d7256f5e13c5d05d02a4bc2264137ab3e132c9f49a73

Transactions (2)

Coinbaseb1a70f6506e578…938100149d04cd

1 in → 21 out9.3500 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb AMW1p9oT…2TzdaZxH AcgDwGo8…BBFwbjVo

77c9ed98d040e5…d391f6f3ab154b

5 in → 14 out40.5173 XPM1.07 KB

AQFkk5xg…PDQYC5kw AFy24Ucy…6i73xkbp APPXRnpg…rBUuW7Fp AefjmuCW…iLY7neu2 AJiSPCty…XjBB6UAz

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.

1.826 × 10⁹⁵(96-digit number)

18266295470499577942…21732690220158863639

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

1.826 × 10⁹⁵(96-digit number)

18266295470499577942…21732690220158863639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.826 × 10⁹⁵(96-digit number)

18266295470499577942…21732690220158863641

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

3.653 × 10⁹⁵(96-digit number)

36532590940999155884…43465380440317727279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.653 × 10⁹⁵(96-digit number)

36532590940999155884…43465380440317727281

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

7.306 × 10⁹⁵(96-digit number)

73065181881998311769…86930760880635454559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.306 × 10⁹⁵(96-digit number)

73065181881998311769…86930760880635454561

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

1.461 × 10⁹⁶(97-digit number)

14613036376399662353…73861521761270909119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.461 × 10⁹⁶(97-digit number)

14613036376399662353…73861521761270909121

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

2.922 × 10⁹⁶(97-digit number)

29226072752799324707…47723043522541818239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.922 × 10⁹⁶(97-digit number)

29226072752799324707…47723043522541818241

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 #432,044

Cookie Preferences