Block #1,567,529

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2016, 3:05:35 PM · Difficulty 10.7586 · 5,259,708 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f435ceba8242a04af63ce7cdbc630f8f5e71d0750f7ef3a912ef942af272bdda

View on Chainz ↗

Height

#1,567,529

Difficulty

10.758648

Transactions

Size

1.28 KB

Version

Bits

0ac236be

Nonce

27,824,377

Timestamp

5/1/2016, 3:05:35 PM

Confirmations

5,259,708

Mined by

⛏️ P2SHALeWmeYHeykSSuqhYGTArX5Kigy1Tr6AUp

Merkle Root

c98972226ed332296117d21b7a807b3958da2d8a204c7da51a1454aaf49e27a4

Transactions (2)

Coinbase2fdd4f1e9486d2…111fbb418e0848

1 in → 1 out8.6500 XPM110 B

ALeWmeYH…y1Tr6AUp

139cd0f0a021df…1336210a3aa6d4

1 in → 28 out185.2743 XPM1.08 KB

AXNE3SK3…8oKZURo4 AQvCUyVa…xah6QwcD ATJdYD4X…Z9xqHf6G AYHE76pQ…KaiLyuM4 AMp8NZmr…fC3UXUSs

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.

1.057 × 10⁹⁷(98-digit number)

10570379425212827648…74073048675533168639

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

1.057 × 10⁹⁷(98-digit number)

10570379425212827648…74073048675533168639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.057 × 10⁹⁷(98-digit number)

10570379425212827648…74073048675533168641

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

2.114 × 10⁹⁷(98-digit number)

21140758850425655297…48146097351066337279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.114 × 10⁹⁷(98-digit number)

21140758850425655297…48146097351066337281

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

4.228 × 10⁹⁷(98-digit number)

42281517700851310595…96292194702132674559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.228 × 10⁹⁷(98-digit number)

42281517700851310595…96292194702132674561

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

8.456 × 10⁹⁷(98-digit number)

84563035401702621191…92584389404265349119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.456 × 10⁹⁷(98-digit number)

84563035401702621191…92584389404265349121

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

1.691 × 10⁹⁸(99-digit number)

16912607080340524238…85168778808530698239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.691 × 10⁹⁸(99-digit number)

16912607080340524238…85168778808530698241

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 #1,567,529

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