Block #105,542

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/8/2013, 2:00:57 PM · Difficulty 9.5866 · 6,698,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4fd364e763f75c982d15a909ae32cc306a2a52e92652dafff4d27c4bc5cb247

View on Chainz ↗

Height

#105,542

Difficulty

9.586620

Transactions

Size

425 B

Version

Bits

09962cbb

Nonce

16,844

Timestamp

8/8/2013, 2:00:57 PM

Confirmations

6,698,243

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

3663575db44ac5963b3435466a574ed261033e4313910de35fba5de57b358739

Transactions (2)

Coinbasec6aca472403421…ca4905f6a330c6

1 in → 1 out10.8800 XPM109 B

ATzEHZ7a…2eAGweip

b7004ce7e54b3d…526943cad4f2ec

1 in → 2 out8.8667 XPM225 B

AYVqDhhc…kpn41wRb AJv5WoqT…tqCRQqFk

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.

1.067 × 10⁹⁶(97-digit number)

10671643079873668349…92172890140277297259

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

1.067 × 10⁹⁶(97-digit number)

10671643079873668349…92172890140277297259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.067 × 10⁹⁶(97-digit number)

10671643079873668349…92172890140277297261

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

2.134 × 10⁹⁶(97-digit number)

21343286159747336699…84345780280554594519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.134 × 10⁹⁶(97-digit number)

21343286159747336699…84345780280554594521

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

4.268 × 10⁹⁶(97-digit number)

42686572319494673399…68691560561109189039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.268 × 10⁹⁶(97-digit number)

42686572319494673399…68691560561109189041

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

8.537 × 10⁹⁶(97-digit number)

85373144638989346798…37383121122218378079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.537 × 10⁹⁶(97-digit number)

85373144638989346798…37383121122218378081

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

1.707 × 10⁹⁷(98-digit number)

17074628927797869359…74766242244436756159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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