Block #574,635

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/3/2014, 11:03:46 AM · Difficulty 10.9678 · 6,233,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

108b6ca658a27bfbfa9ae6d83b98511aaf9019fabe9b5b173dc5a2ff2b162a7b

View on Chainz ↗

Height

#574,635

Difficulty

10.967776

Transactions

Size

562 B

Version

Bits

0af7c027

Nonce

468,846

Timestamp

6/3/2014, 11:03:46 AM

Confirmations

6,233,487

Mined by

⛏️ aShTAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9f74dfaaf4e044a7e2fc87e44147548f40a110d245bed801ffa09d9af977e3ec

Transactions (1)

Coinbase9f74dfaaf4e044…a09d9af977e3ec

1 in → 12 out8.3000 XPM471 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q AQyr8Lw3…hs4nt3Pn

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.

5.715 × 10⁹⁶(97-digit number)

57150897394793845536…51777526877540587939

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

5.715 × 10⁹⁶(97-digit number)

57150897394793845536…51777526877540587939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.715 × 10⁹⁶(97-digit number)

57150897394793845536…51777526877540587941

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

1.143 × 10⁹⁷(98-digit number)

11430179478958769107…03555053755081175879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.143 × 10⁹⁷(98-digit number)

11430179478958769107…03555053755081175881

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

2.286 × 10⁹⁷(98-digit number)

22860358957917538214…07110107510162351759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.286 × 10⁹⁷(98-digit number)

22860358957917538214…07110107510162351761

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

4.572 × 10⁹⁷(98-digit number)

45720717915835076429…14220215020324703519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.572 × 10⁹⁷(98-digit number)

45720717915835076429…14220215020324703521

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

9.144 × 10⁹⁷(98-digit number)

91441435831670152858…28440430040649407039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.144 × 10⁹⁷(98-digit number)

91441435831670152858…28440430040649407041

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

1.828 × 10⁹⁸(99-digit number)

18288287166334030571…56880860081298814079

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 #574,635

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