Block #244,919

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 4:11:05 AM · Difficulty 9.9633 · 6,560,182 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8092c59c050d3a032772923fe383097be0f8952bdb3ffb4d03652fc8de427cea

View on Chainz ↗

Height

#244,919

Difficulty

9.963270

Transactions

Size

2.04 KB

Version

Bits

09f698de

Nonce

39,353

Timestamp

11/5/2013, 4:11:05 AM

Confirmations

6,560,182

Mined by

⛏️ RxoAG4tmsTwdqFKxW6HdzmkPyjcfMYFrtq2r9

Merkle Root

016654a94922fd598bed361c2fbc54d7ed51a7e074db5a7276594094c8bd54ae

Transactions (1)

Coinbase016654a94922fd…594094c8bd54ae

1 in → 57 out10.0243 XPM1.95 KB

AG4tmsTw…YFrtq2r9 ANWcCA1W…FYxSHbqJ AeZmMFY8…mjAy5Mi4 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

2.297 × 10⁹⁷(98-digit number)

22971877019171117760…17635747733525634599

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

2.297 × 10⁹⁷(98-digit number)

22971877019171117760…17635747733525634599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.297 × 10⁹⁷(98-digit number)

22971877019171117760…17635747733525634601

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

4.594 × 10⁹⁷(98-digit number)

45943754038342235521…35271495467051269199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.594 × 10⁹⁷(98-digit number)

45943754038342235521…35271495467051269201

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

9.188 × 10⁹⁷(98-digit number)

91887508076684471042…70542990934102538399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.188 × 10⁹⁷(98-digit number)

91887508076684471042…70542990934102538401

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

1.837 × 10⁹⁸(99-digit number)

18377501615336894208…41085981868205076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.837 × 10⁹⁸(99-digit number)

18377501615336894208…41085981868205076801

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

3.675 × 10⁹⁸(99-digit number)

36755003230673788416…82171963736410153599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.675 × 10⁹⁸(99-digit number)

36755003230673788416…82171963736410153601

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