Block #313,143

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 8:17:08 AM · Difficulty 9.9960 · 6,493,166 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

965f0ea73d917ba26b1b404e5c645f39d84da6ca17e1ff0f1a468728ea2dcb57

View on Chainz ↗

Height

#313,143

Difficulty

9.996033

Transactions

Size

1.15 KB

Version

Bits

09fefc0d

Nonce

182,240

Timestamp

12/15/2013, 8:17:08 AM

Confirmations

6,493,166

Mined by

⛏️ 7aRe{AZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

086b530b8a5adfe443474be7ca48db1ffb7ad08471d6c1dd3a6d75be0154c576

Transactions (1)

Coinbase086b530b8a5adf…6d75be0154c576

1 in → 30 out9.9700 XPM1.06 KB

AZ2pPuKg…95SN2Yr7 Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AayReikY…2HAC42fs AMUqRr2R…WHtMC5U6

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.

1.113 × 10⁹⁸(99-digit number)

11138326618791383581…95536646127434479999

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

1.113 × 10⁹⁸(99-digit number)

11138326618791383581…95536646127434479999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.113 × 10⁹⁸(99-digit number)

11138326618791383581…95536646127434480001

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

2.227 × 10⁹⁸(99-digit number)

22276653237582767162…91073292254868959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.227 × 10⁹⁸(99-digit number)

22276653237582767162…91073292254868960001

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

4.455 × 10⁹⁸(99-digit number)

44553306475165534325…82146584509737919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.455 × 10⁹⁸(99-digit number)

44553306475165534325…82146584509737920001

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

8.910 × 10⁹⁸(99-digit number)

89106612950331068651…64293169019475839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.910 × 10⁹⁸(99-digit number)

89106612950331068651…64293169019475840001

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

1.782 × 10⁹⁹(100-digit number)

17821322590066213730…28586338038951679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.782 × 10⁹⁹(100-digit number)

17821322590066213730…28586338038951680001

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 #313,143

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