Block #1,542,306

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/15/2016, 10:04:48 AM · Difficulty 10.6483 · 5,274,865 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae46fcaeb24f5fa1a58213966184fe9312311b199721b357b6d98eee31fa5faf

View on Chainz ↗

Height

#1,542,306

Difficulty

10.648325

Transactions

Size

1.11 KB

Version

Bits

0aa5f8a6

Nonce

1,966,528,019

Timestamp

4/15/2016, 10:04:48 AM

Confirmations

5,274,865

Mined by

⛏️ P2SHAQfaSMKXiwJXzZhvP4tYaefnzUFiJGPLui

Merkle Root

504177da0b4086568770034d041714d235fe9e010adaa6226b7a154e4f758e51

Transactions (2)

Coinbase0e1247092a6ac4…3e1e91b8c8ccfe

1 in → 1 out8.8200 XPM110 B

AQfaSMKX…FiJGPLui

173e4947f2b2d4…729a7f9a563f98

1 in → 23 out7.9213 XPM939 B

AeUcCSMd…adi9fGPy AGanE1Wb…jpZARgZm ARa3WCyN…njnSFMvF AJRUMD2m…G5eCrAjJ AScLRefc…Gn8wuPKB

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.

5.807 × 10⁹²(93-digit number)

58077737868472707978…23073739957338402719

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

5.807 × 10⁹²(93-digit number)

58077737868472707978…23073739957338402719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.807 × 10⁹²(93-digit number)

58077737868472707978…23073739957338402721

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

1.161 × 10⁹³(94-digit number)

11615547573694541595…46147479914676805439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.161 × 10⁹³(94-digit number)

11615547573694541595…46147479914676805441

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

2.323 × 10⁹³(94-digit number)

23231095147389083191…92294959829353610879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.323 × 10⁹³(94-digit number)

23231095147389083191…92294959829353610881

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

4.646 × 10⁹³(94-digit number)

46462190294778166383…84589919658707221759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.646 × 10⁹³(94-digit number)

46462190294778166383…84589919658707221761

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

9.292 × 10⁹³(94-digit number)

92924380589556332766…69179839317414443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.292 × 10⁹³(94-digit number)

92924380589556332766…69179839317414443521

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

1.858 × 10⁹⁴(95-digit number)

18584876117911266553…38359678634828887039

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

Block #1,542,306

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