Block #203,115

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 3:50:02 PM · Difficulty 9.8965 · 6,591,899 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec20203d0284a05841159173851f871232954d68f5e6e3974a264177febf2189

View on Chainz ↗

Height

#203,115

Difficulty

9.896498

Transactions

Size

767 B

Version

Bits

09e580e7

Nonce

39,573

Timestamp

10/10/2013, 3:50:02 PM

Confirmations

6,591,899

Mined by

⛏️ P2SHAKEpJCHrPDR7GCfYXiEzkNbeEEkzLoh8v9

Merkle Root

f9ee47a82cf6bb8cb98646c243051a7da28df24aa0e5730c03466c0a1c4887a0

Transactions (3)

Coinbasecd726f1bc7233f…2360cca7c64138

1 in → 1 out10.2200 XPM109 B

AKEpJCHr…kzLoh8v9

92e989a121def0…9e45472d01b433

1 in → 1 out2.9928 XPM193 B

ASazCFjo…nA3y7k5f

75eb5b1ab1fee9…6b44fcf6dfcd9f

2 in → 2 out5.6070 XPM374 B

Ab5uypEx…mVqX8FmY AJH8xvRy…4TzqfgQt

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.

1.011 × 10⁹⁶(97-digit number)

10116486173620549840…56384297447356497919

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

1.011 × 10⁹⁶(97-digit number)

10116486173620549840…56384297447356497919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.011 × 10⁹⁶(97-digit number)

10116486173620549840…56384297447356497921

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

2.023 × 10⁹⁶(97-digit number)

20232972347241099680…12768594894712995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.023 × 10⁹⁶(97-digit number)

20232972347241099680…12768594894712995841

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

4.046 × 10⁹⁶(97-digit number)

40465944694482199360…25537189789425991679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.046 × 10⁹⁶(97-digit number)

40465944694482199360…25537189789425991681

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

8.093 × 10⁹⁶(97-digit number)

80931889388964398721…51074379578851983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.093 × 10⁹⁶(97-digit number)

80931889388964398721…51074379578851983361

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

1.618 × 10⁹⁷(98-digit number)

16186377877792879744…02148759157703966719

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