Block #108,664

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/10/2013, 3:13:23 AM · Difficulty 9.6538 · 6,682,330 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cbfc9a7686c9ed4f0dcd19463ee95a078cba146736fcb6857134651da4c225a

View on Chainz ↗

Height

#108,664

Difficulty

9.653775

Transactions

Size

724 B

Version

Bits

09a75dcc

Nonce

137,730

Timestamp

8/10/2013, 3:13:23 AM

Confirmations

6,682,330

Merkle Root

4fd97ad057c493a73daf058edfd9d815ead20f15a2a1e7e49b42181a9ec76d52

Transactions (2)

Coinbase1ca07ee3c70c5a…610076e1dd4ed5

1 in → 1 out10.7200 XPM109 B

AYnPP6jG…Q3sS4Pbg

0e6a21dc104378…a6ee2c604cfaf9

3 in → 2 out771.9707 XPM524 B

AeTFrnko…VSUMnrqp AZG1RyZ2…zxTuJArf

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.

1.917 × 10⁹⁸(99-digit number)

19175608307503512550…49931869592831519419

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

1.917 × 10⁹⁸(99-digit number)

19175608307503512550…49931869592831519419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.917 × 10⁹⁸(99-digit number)

19175608307503512550…49931869592831519421

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

3.835 × 10⁹⁸(99-digit number)

38351216615007025101…99863739185663038839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.835 × 10⁹⁸(99-digit number)

38351216615007025101…99863739185663038841

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

7.670 × 10⁹⁸(99-digit number)

76702433230014050203…99727478371326077679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.670 × 10⁹⁸(99-digit number)

76702433230014050203…99727478371326077681

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

1.534 × 10⁹⁹(100-digit number)

15340486646002810040…99454956742652155359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.534 × 10⁹⁹(100-digit number)

15340486646002810040…99454956742652155361

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

3.068 × 10⁹⁹(100-digit number)

30680973292005620081…98909913485304310719

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