Block #195,703

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 12:02:06 AM · Difficulty 9.8803 · 6,603,291 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

441ab5a4dacc31b25d3f1ed311c956d4bd2918ca04ced42a5b22da535ac2ec1d

View on Chainz ↗

Height

#195,703

Difficulty

9.880276

Transactions

Size

3.97 KB

Version

Bits

09e159bd

Nonce

1,164,749,986

Timestamp

10/6/2013, 12:02:06 AM

Confirmations

6,603,291

Mined by

⛏️ wRP~"AKXD6KoZu6YFqGXmDSyTutF9qVpbKBrJcd

Merkle Root

dcc576af4730b9d7d63957efd87d4e9da4aed5913cbc1488102e10c1689c6ebb

Transactions (1)

Coinbasedcc576af4730b9…2e10c1689c6ebb

1 in → 115 out10.1900 XPM3.88 KB

AKXD6KoZ…pbKBrJcd AR3yVDg3…SFPbbCst ALWSkoC4…zeCoyaty AMse1voq…GntYtmba Ab7ULbjQ…fuVABZZs

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.

6.789 × 10⁹⁴(95-digit number)

67894355331771219233…04131390126045053439

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

6.789 × 10⁹⁴(95-digit number)

67894355331771219233…04131390126045053439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.789 × 10⁹⁴(95-digit number)

67894355331771219233…04131390126045053441

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

1.357 × 10⁹⁵(96-digit number)

13578871066354243846…08262780252090106879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.357 × 10⁹⁵(96-digit number)

13578871066354243846…08262780252090106881

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

2.715 × 10⁹⁵(96-digit number)

27157742132708487693…16525560504180213759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.715 × 10⁹⁵(96-digit number)

27157742132708487693…16525560504180213761

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

5.431 × 10⁹⁵(96-digit number)

54315484265416975386…33051121008360427519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.431 × 10⁹⁵(96-digit number)

54315484265416975386…33051121008360427521

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

1.086 × 10⁹⁶(97-digit number)

10863096853083395077…66102242016720855039

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