Block #320,246

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 12:52:43 PM · Difficulty 10.1815 · 6,479,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c221be63e672c35e32ceda80ca07d6ea24aaa4401e93fa930bb5b1810979f0d

View on Chainz ↗

Height

#320,246

Difficulty

10.181462

Transactions

Size

879 B

Version

Bits

0a2e744e

Nonce

153,088

Timestamp

12/19/2013, 12:52:43 PM

Confirmations

6,479,225

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

949b17f2896ba09063e2dea00d2cc3cdd0e4a59a361d9d2e9791464e796cc7f6

Transactions (4)

Coinbase61cc20a3752c2c…31d07dd4d55a15

1 in → 1 out9.6600 XPM110 B

AeKNrjNj…1NEq95Ta

16ad992a85172d…89f006e0e90e60

1 in → 2 out6.2755 XPM226 B

Ad7hXpcH…FYgweVmY ARbfFkV5…475TFWd2

195daccf12698f…056105e9faa06e

1 in → 2 out6.0403 XPM225 B

AaP3Ex2W…xfJuevuy AKmxBBzd…AHmu4uiE

767c48dd159c1c…6a43cedd458814

1 in → 2 out5.8904 XPM226 B

AWmdPZdz…8mW9CDbS AK2aKECs…tcgLXEJv

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.

3.965 × 10⁹⁸(99-digit number)

39659916049229001794…09606303198308920319

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

3.965 × 10⁹⁸(99-digit number)

39659916049229001794…09606303198308920319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.965 × 10⁹⁸(99-digit number)

39659916049229001794…09606303198308920321

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

7.931 × 10⁹⁸(99-digit number)

79319832098458003589…19212606396617840639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.931 × 10⁹⁸(99-digit number)

79319832098458003589…19212606396617840641

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

1.586 × 10⁹⁹(100-digit number)

15863966419691600717…38425212793235681279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.586 × 10⁹⁹(100-digit number)

15863966419691600717…38425212793235681281

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

3.172 × 10⁹⁹(100-digit number)

31727932839383201435…76850425586471362559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.172 × 10⁹⁹(100-digit number)

31727932839383201435…76850425586471362561

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

6.345 × 10⁹⁹(100-digit number)

63455865678766402871…53700851172942725119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.345 × 10⁹⁹(100-digit number)

63455865678766402871…53700851172942725121

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