Block #116,323

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/14/2013, 8:30:59 AM · Difficulty 9.7473 · 6,701,181 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ca8ed17fa19453841d301b2c2ca7155800a25c812decb2f355d3d4bc938cbf0a

View on Chainz ↗

Height

#116,323

Difficulty

9.747303

Transactions

Size

201 B

Version

Bits

09bf4f40

Nonce

42,166

Timestamp

8/14/2013, 8:30:59 AM

Confirmations

6,701,181

Mined by

⛏️ P2SHAKErQXMSbzQTkoT3CyUmWJvi8LJWgaCTzm

Merkle Root

f568bd8c54b941ea61d14db625f7691d75f08e41159067e65266b5ae808a8be9

Transactions (1)

Coinbasef568bd8c54b941…66b5ae808a8be9

1 in → 1 out10.5100 XPM109 B

AKErQXMS…JWgaCTzm

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.

1.176 × 10⁹⁹(100-digit number)

11768150428170813776…81727334458732334289

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

1.176 × 10⁹⁹(100-digit number)

11768150428170813776…81727334458732334289

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.176 × 10⁹⁹(100-digit number)

11768150428170813776…81727334458732334291

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

2.353 × 10⁹⁹(100-digit number)

23536300856341627552…63454668917464668579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.353 × 10⁹⁹(100-digit number)

23536300856341627552…63454668917464668581

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

4.707 × 10⁹⁹(100-digit number)

47072601712683255105…26909337834929337159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.707 × 10⁹⁹(100-digit number)

47072601712683255105…26909337834929337161

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

9.414 × 10⁹⁹(100-digit number)

94145203425366510210…53818675669858674319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.414 × 10⁹⁹(100-digit number)

94145203425366510210…53818675669858674321

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

1.882 × 10¹⁰⁰(101-digit number)

18829040685073302042…07637351339717348639

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 #116,323

Cookie Preferences