Block #643,982

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/22/2014, 10:04:36 PM · Difficulty 10.9554 · 6,172,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7813e300aeea27a9db2e78a0a020086495e73aa032b5dc8145e66e8283c48084

View on Chainz ↗

Height

#643,982

Difficulty

10.955422

Transactions

Size

777 B

Version

Bits

0af49685

Nonce

1,245,485,787

Timestamp

7/22/2014, 10:04:36 PM

Confirmations

6,172,883

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

429daa6a54680fe291800bb88c0c15b718597c9ddf28265b46a20a499f4991f9

Transactions (3)

Coinbaseda745cc3a33355…6464740ccef753

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

2f9c4b9e1be897…ebcd2a03d4e816

2 in → 2 out10.1862 XPM376 B

AcwovHdS…v48xVTF4 AJzjuYh3…ndhqFVng

aa2db49d0f3de7…8fd59891fa67c9

1 in → 1 out7.8845 XPM193 B

AbnVNvbH…WBFv1MST

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.

2.937 × 10⁹⁸(99-digit number)

29375013893625205505…71528368707867852799

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

2.937 × 10⁹⁸(99-digit number)

29375013893625205505…71528368707867852799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.937 × 10⁹⁸(99-digit number)

29375013893625205505…71528368707867852801

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

5.875 × 10⁹⁸(99-digit number)

58750027787250411010…43056737415735705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.875 × 10⁹⁸(99-digit number)

58750027787250411010…43056737415735705601

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

1.175 × 10⁹⁹(100-digit number)

11750005557450082202…86113474831471411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.175 × 10⁹⁹(100-digit number)

11750005557450082202…86113474831471411201

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

2.350 × 10⁹⁹(100-digit number)

23500011114900164404…72226949662942822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.350 × 10⁹⁹(100-digit number)

23500011114900164404…72226949662942822401

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

4.700 × 10⁹⁹(100-digit number)

47000022229800328808…44453899325885644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.700 × 10⁹⁹(100-digit number)

47000022229800328808…44453899325885644801

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

9.400 × 10⁹⁹(100-digit number)

94000044459600657617…88907798651771289599

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 #643,982

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