Block #314,989

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 6:47:16 AM · Difficulty 10.0814 · 6,488,539 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

190a085ce20ded03b0781c065b3c6b05f83ecd6ccdab7d21859e3b366ba094e4

View on Chainz ↗

Height

#314,989

Difficulty

10.081423

Transactions

Size

1.05 KB

Version

Bits

0a14d82a

Nonce

36,849

Timestamp

12/16/2013, 6:47:16 AM

Confirmations

6,488,539

Mined by

⛏️ maRAZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

11ec92b55cc858cba8985f27234a48591153721667963f8117f2e38ff8189ca7

Transactions (1)

Coinbase11ec92b55cc858…f2e38ff8189ca7

1 in → 27 out9.8200 XPM981 B

AZ2pPuKg…95SN2Yr7 Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AVWTuF2g…JyhYqGF5 AH3Qkpre…d9jSDwSX

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.

1.943 × 10⁹⁹(100-digit number)

19432474107726200449…76928973948483650559

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

1.943 × 10⁹⁹(100-digit number)

19432474107726200449…76928973948483650559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.943 × 10⁹⁹(100-digit number)

19432474107726200449…76928973948483650561

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

3.886 × 10⁹⁹(100-digit number)

38864948215452400898…53857947896967301119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.886 × 10⁹⁹(100-digit number)

38864948215452400898…53857947896967301121

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

7.772 × 10⁹⁹(100-digit number)

77729896430904801797…07715895793934602239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.772 × 10⁹⁹(100-digit number)

77729896430904801797…07715895793934602241

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

1.554 × 10¹⁰⁰(101-digit number)

15545979286180960359…15431791587869204479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.554 × 10¹⁰⁰(101-digit number)

15545979286180960359…15431791587869204481

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

3.109 × 10¹⁰⁰(101-digit number)

31091958572361920718…30863583175738408959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.109 × 10¹⁰⁰(101-digit number)

31091958572361920718…30863583175738408961

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