Block #254,294

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 3:24:55 PM · Difficulty 9.9730 · 6,556,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4cba902826b6ffb36a32d4a139471c880a306e046cf5712b7e0b124f183bf9b8

View on Chainz ↗

Height

#254,294

Difficulty

9.973026

Transactions

Size

1.97 KB

Version

Bits

09f9183d

Nonce

61,309

Timestamp

11/10/2013, 3:24:55 PM

Confirmations

6,556,482

Mined by

⛏️ VaR.ATnFXhYbVwMmLNHfrWSkQM8yiQJqjrGzMC

Merkle Root

8343638956955e9eabe9d9ac880425cfa1f6cd6b795cab46b6e936f44288ca5a

Transactions (1)

Coinbase8343638956955e…e936f44288ca5a

1 in → 55 out10.0200 XPM1.89 KB

ATnFXhYb…JqjrGzMC AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AHkgKuuD…TkWqWiw1 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.

2.496 × 10⁹¹(92-digit number)

24965139623662927622…87728912039962790569

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

2.496 × 10⁹¹(92-digit number)

24965139623662927622…87728912039962790569

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.496 × 10⁹¹(92-digit number)

24965139623662927622…87728912039962790571

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

4.993 × 10⁹¹(92-digit number)

49930279247325855244…75457824079925581139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.993 × 10⁹¹(92-digit number)

49930279247325855244…75457824079925581141

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

9.986 × 10⁹¹(92-digit number)

99860558494651710488…50915648159851162279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.986 × 10⁹¹(92-digit number)

99860558494651710488…50915648159851162281

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

1.997 × 10⁹²(93-digit number)

19972111698930342097…01831296319702324559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.997 × 10⁹²(93-digit number)

19972111698930342097…01831296319702324561

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

3.994 × 10⁹²(93-digit number)

39944223397860684195…03662592639404649119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.994 × 10⁹²(93-digit number)

39944223397860684195…03662592639404649121

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

Block #254,294

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