Block #1,432,547

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2016, 9:25:22 AM · Difficulty 10.7869 · 5,410,609 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b0001e28e5586bb7dc61ec91ad1aede5de00c13c2fca2bb632c42776c9a8876

View on Chainz ↗

Height

#1,432,547

Difficulty

10.786925

Transactions

Size

2.95 KB

Version

Bits

0ac973e7

Nonce

330,288,968

Timestamp

1/28/2016, 9:25:22 AM

Confirmations

5,410,609

Mined by

⛏️ P2SHAZpzpMbcTiabPMcE6HKsq7pKwy8qAnxPhN

Merkle Root

9be7d829361eca68688b2136f5d6dd06a49b0ce79b1ac20cfc5f36c8c7c8ffd8

Transactions (3)

Coinbase1d0ff70f531848…f6473fd8cc970c

1 in → 1 out8.6200 XPM110 B

AZpzpMbc…8qAnxPhN

557143f0779761…7da05d68c875ed

17 in → 2 out400.0000 XPM2.54 KB

AVe4tjpY…A89cS77a AcDhjHA9…ebukETHz

426c6b719a3de0…f75ffbe0e2377f

1 in → 2 out516.3203 XPM226 B

AHNkwmbJ…EUxEmniY AYkhUQM3…k4nwtT6s

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.

9.312 × 10⁹⁶(97-digit number)

93124638540210389843…06892833225165987839

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

9.312 × 10⁹⁶(97-digit number)

93124638540210389843…06892833225165987839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.312 × 10⁹⁶(97-digit number)

93124638540210389843…06892833225165987841

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

1.862 × 10⁹⁷(98-digit number)

18624927708042077968…13785666450331975679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.862 × 10⁹⁷(98-digit number)

18624927708042077968…13785666450331975681

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

3.724 × 10⁹⁷(98-digit number)

37249855416084155937…27571332900663951359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.724 × 10⁹⁷(98-digit number)

37249855416084155937…27571332900663951361

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

7.449 × 10⁹⁷(98-digit number)

74499710832168311874…55142665801327902719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.449 × 10⁹⁷(98-digit number)

74499710832168311874…55142665801327902721

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

1.489 × 10⁹⁸(99-digit number)

14899942166433662374…10285331602655805439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.489 × 10⁹⁸(99-digit number)

14899942166433662374…10285331602655805441

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 #1,432,547

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