Block #308,151

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 11:04:22 PM · Difficulty 9.9944 · 6,505,931 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23443fdc2c015011c34833802a50b879aa71d4c2d8b12c75b48efe1901af17b6

View on Chainz ↗

Height

#308,151

Difficulty

9.994417

Transactions

Size

1.05 KB

Version

Bits

09fe921a

Nonce

7,027

Timestamp

12/12/2013, 11:04:22 PM

Confirmations

6,505,931

Mined by

⛏️ aR@AMttQDuftdpMyrb199TXiUSH5L7j6tfS9x

Merkle Root

0d48ff1207d402cfc21285307173584984f04f20312cd341a902366acf1d16c6

Transactions (1)

Coinbase0d48ff1207d402…02366acf1d16c6

1 in → 27 out10.0000 XPM981 B

AMttQDuf…7j6tfS9x AMbCuLHZ…WSoStwkc Aac9Hjdg…P4ktypc3 AWXYBWKP…qQAoisBJ ANEJ2uT8…YefcaoXo

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.

1.044 × 10⁹⁷(98-digit number)

10443842265948514089…61220391912209478399

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

1.044 × 10⁹⁷(98-digit number)

10443842265948514089…61220391912209478399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.044 × 10⁹⁷(98-digit number)

10443842265948514089…61220391912209478401

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

2.088 × 10⁹⁷(98-digit number)

20887684531897028179…22440783824418956799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.088 × 10⁹⁷(98-digit number)

20887684531897028179…22440783824418956801

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

4.177 × 10⁹⁷(98-digit number)

41775369063794056358…44881567648837913599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.177 × 10⁹⁷(98-digit number)

41775369063794056358…44881567648837913601

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

8.355 × 10⁹⁷(98-digit number)

83550738127588112716…89763135297675827199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.355 × 10⁹⁷(98-digit number)

83550738127588112716…89763135297675827201

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

1.671 × 10⁹⁸(99-digit number)

16710147625517622543…79526270595351654399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.671 × 10⁹⁸(99-digit number)

16710147625517622543…79526270595351654401

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

Block #308,151

Cookie Preferences