Block #108,316

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/9/2013, 11:24:34 PM · Difficulty 9.6455 · 6,702,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b500006a09cbc128afb0e199d9bbf9344c297586eb76494aa74e7c80052d3cc

View on Chainz ↗

Height

#108,316

Difficulty

9.645471

Transactions

Size

1.27 KB

Version

Bits

09a53d9b

Nonce

27,197

Timestamp

8/9/2013, 11:24:34 PM

Confirmations

6,702,258

Mined by

⛏️ P2SHAGptBojqqQouFV9jCPkKx6mdwp8sPdcmq7

Merkle Root

e96b2de24836afdcfb9d4b8c0b5fdedd45800c283431f6e065645f3edc2ed46b

Transactions (2)

Coinbaseceaeb162709c8f…92ac8796e3c0de

1 in → 1 out10.7500 XPM109 B

AGptBojq…8sPdcmq7

feb756a212578b…746ca12dd46371

9 in → 2 out99.4400 XPM1.08 KB

AdNeXXkk…QpfXAns4 AXoGBtgj…eiSiHBtd

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.

1.494 × 10⁹⁵(96-digit number)

14947762585938844602…77254331417461699739

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

1.494 × 10⁹⁵(96-digit number)

14947762585938844602…77254331417461699739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.494 × 10⁹⁵(96-digit number)

14947762585938844602…77254331417461699741

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

2.989 × 10⁹⁵(96-digit number)

29895525171877689204…54508662834923399479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.989 × 10⁹⁵(96-digit number)

29895525171877689204…54508662834923399481

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

5.979 × 10⁹⁵(96-digit number)

59791050343755378409…09017325669846798959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.979 × 10⁹⁵(96-digit number)

59791050343755378409…09017325669846798961

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

1.195 × 10⁹⁶(97-digit number)

11958210068751075681…18034651339693597919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.195 × 10⁹⁶(97-digit number)

11958210068751075681…18034651339693597921

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

2.391 × 10⁹⁶(97-digit number)

23916420137502151363…36069302679387195839

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

Block #108,316

Cookie Preferences