Block #308,936

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 8:44:38 AM · Difficulty 9.9947 · 6,485,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecd765afdb70dc4ea4e84903c0e940a5172b761bdaf60a30d53f76602607a099

View on Chainz ↗

Height

#308,936

Difficulty

9.994663

Transactions

Size

4.64 KB

Version

Bits

09fea242

Nonce

Timestamp

12/13/2013, 8:44:38 AM

Confirmations

6,485,272

Merkle Root

c4de855dd9210359dd1ea07beb1c1c80cbbe708946a75d3452e20f815b21c0a1

Transactions (4)

Coinbase0ac34cad9167ff…dd94e7493c5514

1 in → 28 out9.9800 XPM1015 B

AJVaFPL7…9MJKAa55 ANNg88pG…ppn21sTe AQDGVS66…1PTWdWkm Aac9Hjdg…P4ktypc3 AZ2pPuKg…95SN2Yr7

5b5e79eba2a09c…bcaf15b1aad2f8

21 in → 2 out20.0143 XPM3.12 KB

Ac1jNHUy…DBU7Czk7 ASfGZvCk…utxVKgjy

cf9e4361bb2805…c1814ce6d86ba7

1 in → 2 out3.6273 XPM226 B

ALEfv71N…MJdhEXXi APzp65Hx…bzzpaqgx

e197e6e2ed323a…b974408e4745f2

1 in → 2 out1.7265 XPM225 B

AVSSoqRA…aFjFn3Zm AWaVot2T…DAxQhUGw

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.

1.164 × 10⁹⁵(96-digit number)

11641191578289115920…59896263702057987679

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

1.164 × 10⁹⁵(96-digit number)

11641191578289115920…59896263702057987679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.164 × 10⁹⁵(96-digit number)

11641191578289115920…59896263702057987681

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

2.328 × 10⁹⁵(96-digit number)

23282383156578231840…19792527404115975359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.328 × 10⁹⁵(96-digit number)

23282383156578231840…19792527404115975361

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

4.656 × 10⁹⁵(96-digit number)

46564766313156463681…39585054808231950719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.656 × 10⁹⁵(96-digit number)

46564766313156463681…39585054808231950721

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

9.312 × 10⁹⁵(96-digit number)

93129532626312927362…79170109616463901439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.312 × 10⁹⁵(96-digit number)

93129532626312927362…79170109616463901441

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

1.862 × 10⁹⁶(97-digit number)

18625906525262585472…58340219232927802879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.862 × 10⁹⁶(97-digit number)

18625906525262585472…58340219232927802881

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