Block #339,668

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 6:40:56 AM · Difficulty 10.1273 · 6,466,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3dfd3a6eeea653f4c376b8d125972de52034ece6f674b0dca267167037dbf090

View on Chainz ↗

Height

#339,668

Difficulty

10.127261

Transactions

Size

2.72 KB

Version

Bits

0a20942c

Nonce

2,467

Timestamp

1/2/2014, 6:40:56 AM

Confirmations

6,466,131

Mined by

⛏️ .aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

29f47e59600aaa63f3c71a707123e263cdd1f02ee3e0db33ce57ec6bc1a95645

Transactions (4)

Coinbase9c74f64e9c61f3…b15adaffa65d73

1 in → 27 out9.7400 XPM981 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AJzWx2VD…j4ZSMit5 AZ2pPuKg…95SN2Yr7

d08b24e8156427…6b5d7bc63de967

8 in → 2 out25.0670 XPM1.23 KB

AYY8V6MN…WRkfm4q8 AG8D9dT7…eGUdoaqH

c761e92574166e…0144a4e836c486

1 in → 2 out1.0546 XPM226 B

AaJmRkLe…Gavwqx7a AeR5t8oH…WF27jDG3

6ba0861912f64d…78db1c34081396

1 in → 2 out4.3894 XPM226 B

ATmA1mLY…iUzzhM3S AMRhhevE…XsBq2Uw5

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.

1.276 × 10⁹⁷(98-digit number)

12760802219868667845…90210908212230362919

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

1.276 × 10⁹⁷(98-digit number)

12760802219868667845…90210908212230362919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.276 × 10⁹⁷(98-digit number)

12760802219868667845…90210908212230362921

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

2.552 × 10⁹⁷(98-digit number)

25521604439737335691…80421816424460725839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.552 × 10⁹⁷(98-digit number)

25521604439737335691…80421816424460725841

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

5.104 × 10⁹⁷(98-digit number)

51043208879474671383…60843632848921451679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.104 × 10⁹⁷(98-digit number)

51043208879474671383…60843632848921451681

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

1.020 × 10⁹⁸(99-digit number)

10208641775894934276…21687265697842903359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10⁹⁸(99-digit number)

10208641775894934276…21687265697842903361

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

2.041 × 10⁹⁸(99-digit number)

20417283551789868553…43374531395685806719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.041 × 10⁹⁸(99-digit number)

20417283551789868553…43374531395685806721

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