Block #317,984

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2013, 1:49:03 AM · Difficulty 10.1546 · 6,496,111 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43c4da7013cff4e5703a80c89c567573b543ff64071ace00770f863662b00fed

View on Chainz ↗

Height

#317,984

Difficulty

10.154555

Transactions

Size

1.04 KB

Version

Bits

0a2790e7

Nonce

109,281

Timestamp

12/18/2013, 1:49:03 AM

Confirmations

6,496,111

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

108f75bada734179f2ad1390bb1981d87ec6cd813acf6cc3a4225d882735bc54

Transactions (1)

Coinbase108f75bada7341…225d882735bc54

1 in → 27 out9.6800 XPM981 B

Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG Ad9pSzHt…cpJ3y2zz AP5UvYhU…vLTDwkdA AKzkYQaQ…zR4FspJZ

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.

7.047 × 10⁹²(93-digit number)

70470033304892447749…57659693200603846399

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

7.047 × 10⁹²(93-digit number)

70470033304892447749…57659693200603846399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.047 × 10⁹²(93-digit number)

70470033304892447749…57659693200603846401

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

1.409 × 10⁹³(94-digit number)

14094006660978489549…15319386401207692799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.409 × 10⁹³(94-digit number)

14094006660978489549…15319386401207692801

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

2.818 × 10⁹³(94-digit number)

28188013321956979099…30638772802415385599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.818 × 10⁹³(94-digit number)

28188013321956979099…30638772802415385601

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

5.637 × 10⁹³(94-digit number)

56376026643913958199…61277545604830771199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.637 × 10⁹³(94-digit number)

56376026643913958199…61277545604830771201

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

1.127 × 10⁹⁴(95-digit number)

11275205328782791639…22555091209661542399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.127 × 10⁹⁴(95-digit number)

11275205328782791639…22555091209661542401

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 #317,984

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