Block #256,031

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 1:55:02 PM · Difficulty 9.9750 · 6,547,206 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e67604381ced80f44b16f9303ae619669926d6d6d7d7fc17d0cd5cd704f9bbc

View on Chainz ↗

Height

#256,031

Difficulty

9.974982

Transactions

Size

1.91 KB

Version

Bits

09f9986e

Nonce

3,834

Timestamp

11/11/2013, 1:55:02 PM

Confirmations

6,547,206

Mined by

⛏️ aR5AGbRhLj1HQi4pXYvW1G5HRrmefnZcEQFqQ

Merkle Root

e207bbd70c66d3448cd6d1d687d843a58561d1b3a7f9274462e12c47753d0c0f

Transactions (1)

Coinbasee207bbd70c66d3…e12c47753d0c0f

1 in → 53 out10.0200 XPM1.82 KB

AGbRhLj1…nZcEQFqQ AFqKfjez…qX9Ace3g AdL4ZZDR…2eQtg1T9 AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5

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.

4.609 × 10⁹¹(92-digit number)

46092163262625299959…95498540087118839999

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

4.609 × 10⁹¹(92-digit number)

46092163262625299959…95498540087118839999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.609 × 10⁹¹(92-digit number)

46092163262625299959…95498540087118840001

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

9.218 × 10⁹¹(92-digit number)

92184326525250599919…90997080174237679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.218 × 10⁹¹(92-digit number)

92184326525250599919…90997080174237680001

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

1.843 × 10⁹²(93-digit number)

18436865305050119983…81994160348475359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.843 × 10⁹²(93-digit number)

18436865305050119983…81994160348475360001

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

3.687 × 10⁹²(93-digit number)

36873730610100239967…63988320696950719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.687 × 10⁹²(93-digit number)

36873730610100239967…63988320696950720001

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

7.374 × 10⁹²(93-digit number)

73747461220200479935…27976641393901439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.374 × 10⁹²(93-digit number)

73747461220200479935…27976641393901440001

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