Block #245,690

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 3:20:01 PM · Difficulty 9.9640 · 6,557,698 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c6aba8bca1be4e7594ba11defcc21fa45fca5d465cd5fd887ef690f84a13cfd

View on Chainz ↗

Height

#245,690

Difficulty

9.964008

Transactions

Size

1.79 KB

Version

Bits

09f6c942

Nonce

16,915

Timestamp

11/5/2013, 3:20:01 PM

Confirmations

6,557,698

Mined by

⛏️ P2SHAGssgv8CenT6oWQcceq6rFxSyqzT3wunSb

Merkle Root

80640aa69731f19cac590134de9f5265c1e08694be1fbb8d0add3711953a451e

Transactions (5)

Coinbasef306e003c4b96d…dfa8ebbb6bd7a3

1 in → 1 out10.1100 XPM109 B

AGssgv8C…zT3wunSb

94cfbb5b0be6bc…3afec559c8e2e5

4 in → 2 out280.3927 XPM668 B

AK3Lao44…kfsg5ztV AdaPDrK2…SpcVbzha

d11f39bb24e553…41c820d177ee44

1 in → 2 out5.1382 XPM226 B

AYmqUaw8…zi7mGzwn AXPmta1o…aQUpRtjh

f0c15f107f9fb6…67f86ff17e7fa7

1 in → 2 out3.1514 XPM226 B

ALsqSwWV…uZ7sTz8x APGJtNLx…mcbDwodz

6c548007dd6d8d…eb42b052ba5fc4

3 in → 2 out5.0902 XPM519 B

AbZ3dNtr…KZRR1GBe AN3QK9wE…SHQv3wVg

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.

7.030 × 10⁹²(93-digit number)

70300929253090263284…26082892471361846079

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

7.030 × 10⁹²(93-digit number)

70300929253090263284…26082892471361846079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.030 × 10⁹²(93-digit number)

70300929253090263284…26082892471361846081

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

1.406 × 10⁹³(94-digit number)

14060185850618052656…52165784942723692159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.406 × 10⁹³(94-digit number)

14060185850618052656…52165784942723692161

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

2.812 × 10⁹³(94-digit number)

28120371701236105313…04331569885447384319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.812 × 10⁹³(94-digit number)

28120371701236105313…04331569885447384321

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

5.624 × 10⁹³(94-digit number)

56240743402472210627…08663139770894768639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.624 × 10⁹³(94-digit number)

56240743402472210627…08663139770894768641

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

1.124 × 10⁹⁴(95-digit number)

11248148680494442125…17326279541789537279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.124 × 10⁹⁴(95-digit number)

11248148680494442125…17326279541789537281

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