Block #337,981

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/1/2014, 2:40:17 AM · Difficulty 10.1248 · 6,457,996 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76acaba0bced2a7dca16d5218f48b1a5793f5d3e36bd1adae12fd7d960b529c0

View on Chainz ↗

Height

#337,981

Difficulty

10.124835

Transactions

Size

936 B

Version

Bits

0a1ff52b

Nonce

17,825

Timestamp

1/1/2014, 2:40:17 AM

Confirmations

6,457,996

Mined by

AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

dccb1ee3c1232dfc8c83d1bb074bdfc1e1b6950c717eaa237ce25e1c027f578f

Transactions (1)

Coinbasedccb1ee3c1232d…e25e1c027f578f

1 in → 23 out9.7400 XPM845 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 APSP8Z4Y…LWaGMpdL

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.

1.256 × 10⁹⁶(97-digit number)

12564570799479376711…00473702016026883199

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

1.256 × 10⁹⁶(97-digit number)

12564570799479376711…00473702016026883199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.256 × 10⁹⁶(97-digit number)

12564570799479376711…00473702016026883201

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

2.512 × 10⁹⁶(97-digit number)

25129141598958753422…00947404032053766399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.512 × 10⁹⁶(97-digit number)

25129141598958753422…00947404032053766401

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

5.025 × 10⁹⁶(97-digit number)

50258283197917506844…01894808064107532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.025 × 10⁹⁶(97-digit number)

50258283197917506844…01894808064107532801

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

1.005 × 10⁹⁷(98-digit number)

10051656639583501368…03789616128215065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.005 × 10⁹⁷(98-digit number)

10051656639583501368…03789616128215065601

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

2.010 × 10⁹⁷(98-digit number)

20103313279167002737…07579232256430131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.010 × 10⁹⁷(98-digit number)

20103313279167002737…07579232256430131201

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