Block #308,152

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 11:05:15 PM · Difficulty 9.9944 · 6,494,782 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26079fdd81cbd60cb58dbbae8c89437daa8480a8d90dec92ff8452974b4e07e0

View on Chainz ↗

Height

#308,152

Difficulty

9.994417

Transactions

Size

1.08 KB

Version

Bits

09fe921a

Nonce

4,602

Timestamp

12/12/2013, 11:05:15 PM

Confirmations

6,494,782

Mined by

⛏️ aRAAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

a71c9bb74847ed099c999105df886c2c66a2f5053b7ba12edfe053f8823f38e7

Transactions (1)

Coinbasea71c9bb74847ed…e053f8823f38e7

1 in → 28 out9.9800 XPM1015 B

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AMdvB6BS…DPq9FYdA AHAi4PDp…e5tL4csy

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.

4.279 × 10⁹⁹(100-digit number)

42797142607698602158…74347061987716190079

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

4.279 × 10⁹⁹(100-digit number)

42797142607698602158…74347061987716190079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.279 × 10⁹⁹(100-digit number)

42797142607698602158…74347061987716190081

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

8.559 × 10⁹⁹(100-digit number)

85594285215397204317…48694123975432380159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.559 × 10⁹⁹(100-digit number)

85594285215397204317…48694123975432380161

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

1.711 × 10¹⁰⁰(101-digit number)

17118857043079440863…97388247950864760319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.711 × 10¹⁰⁰(101-digit number)

17118857043079440863…97388247950864760321

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

3.423 × 10¹⁰⁰(101-digit number)

34237714086158881727…94776495901729520639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.423 × 10¹⁰⁰(101-digit number)

34237714086158881727…94776495901729520641

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

6.847 × 10¹⁰⁰(101-digit number)

68475428172317763454…89552991803459041279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.847 × 10¹⁰⁰(101-digit number)

68475428172317763454…89552991803459041281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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