Block #255,419

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 6:26:07 AM · Difficulty 9.9742 · 6,587,882 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4c40d3f11b407d82f6495f6caf89d6d6d67220e9defe33800afa319385b749c

View on Chainz ↗

Height

#255,419

Difficulty

9.974231

Transactions

Size

1.71 KB

Version

Bits

09f96739

Nonce

83,707

Timestamp

11/11/2013, 6:26:07 AM

Confirmations

6,587,882

Mined by

⛏️ aRxJAThYr9m5A6v9AW6cmefcvXDPk2KGSuN7FQ

Merkle Root

3eebf337655c0b42916791a0a6a6029ac02feb0dcf275d93be8d9e7bbafe4ee7

Transactions (1)

Coinbase3eebf337655c0b…8d9e7bbafe4ee7

1 in → 47 out10.0200 XPM1.62 KB

AThYr9m5…KGSuN7FQ AXDu24HR…L9o8sC5D AQtzUSwq…htAuF3yC AJ3s18rA…6vFG7H41 AKDTDDtx…iqvw9cdY

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.

1.300 × 10⁹⁵(96-digit number)

13004130018004282324…21177707886075957759

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

1.300 × 10⁹⁵(96-digit number)

13004130018004282324…21177707886075957759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.300 × 10⁹⁵(96-digit number)

13004130018004282324…21177707886075957761

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

2.600 × 10⁹⁵(96-digit number)

26008260036008564648…42355415772151915519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.600 × 10⁹⁵(96-digit number)

26008260036008564648…42355415772151915521

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

5.201 × 10⁹⁵(96-digit number)

52016520072017129297…84710831544303831039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.201 × 10⁹⁵(96-digit number)

52016520072017129297…84710831544303831041

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

1.040 × 10⁹⁶(97-digit number)

10403304014403425859…69421663088607662079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.040 × 10⁹⁶(97-digit number)

10403304014403425859…69421663088607662081

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

2.080 × 10⁹⁶(97-digit number)

20806608028806851718…38843326177215324159

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 #255,419

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