Block #195

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/7/2013, 9:26:37 PM · Difficulty 7.0044 · 6,789,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad807d1044ce4444a137b77659aa056d40896430d66a4a398061e0d842a6154a

View on Chainz ↗

Height

#195

Difficulty

7.004364

Transactions

Size

202 B

Version

Bits

07011e04

Nonce

843

Timestamp

7/7/2013, 9:26:37 PM

Confirmations

6,789,000

Merkle Root

3620de845cafbc60314dc3b016d0e1c5d74a55d3c2920a120d03eede0c6603c3

Transactions (1)

Coinbase3620de845cafbc…03eede0c6603c3

1 in → 1 out20.3600 XPM108 B

AcbjTSnH…UanKKtTP

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.

1.953 × 10¹⁰⁵(106-digit number)

19532048387057408545…04332319797052967679

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

1.953 × 10¹⁰⁵(106-digit number)

19532048387057408545…04332319797052967679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.953 × 10¹⁰⁵(106-digit number)

19532048387057408545…04332319797052967681

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

3.906 × 10¹⁰⁵(106-digit number)

39064096774114817091…08664639594105935359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.906 × 10¹⁰⁵(106-digit number)

39064096774114817091…08664639594105935361

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

7.812 × 10¹⁰⁵(106-digit number)

78128193548229634183…17329279188211870719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.812 × 10¹⁰⁵(106-digit number)

78128193548229634183…17329279188211870721

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

1.562 × 10¹⁰⁶(107-digit number)

15625638709645926836…34658558376423741439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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