Block #673,834

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/11/2014, 8:25:31 PM · Difficulty 10.9653 · 6,134,190 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04ea154b7e3dd884b813c2f18775e4a888c4220932bba47dabd941fb6a98ce58

View on Chainz ↗

Height

#673,834

Difficulty

10.965291

Transactions

Size

1.01 KB

Version

Bits

0af71d48

Nonce

2,137,856,663

Timestamp

8/11/2014, 8:25:31 PM

Confirmations

6,134,190

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0ec0f9565d536ba950f0f078f5e37d50e0089a3bb69430ffd10cedf73c685e58

Transactions (4)

Coinbase590e8d49842331…5f39b8216b9c0c

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

89e5f023c4e1f1…955853d459a4a2

1 in → 2 out5.6375 XPM226 B

AdBMeV6y…8G7oZQ9C AcKerPva…qeeuPChG

eb66c2f184f2fa…fe5bb83de3440d

1 in → 2 out2.9554 XPM225 B

AXme6eTz…PLdysKBL AVRzbFjr…z77EeBtk

6a5fc897b85edf…dbc84838152277

2 in → 2 out1.1063 XPM375 B

Abs1CTRR…uk6ieBYF AMSrahh7…WWJEaAVh

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.

3.150 × 10⁹⁹(100-digit number)

31508388588633958637…20427957962374184959

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

3.150 × 10⁹⁹(100-digit number)

31508388588633958637…20427957962374184959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.150 × 10⁹⁹(100-digit number)

31508388588633958637…20427957962374184961

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

6.301 × 10⁹⁹(100-digit number)

63016777177267917275…40855915924748369919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.301 × 10⁹⁹(100-digit number)

63016777177267917275…40855915924748369921

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

1.260 × 10¹⁰⁰(101-digit number)

12603355435453583455…81711831849496739839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.260 × 10¹⁰⁰(101-digit number)

12603355435453583455…81711831849496739841

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

2.520 × 10¹⁰⁰(101-digit number)

25206710870907166910…63423663698993479679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.520 × 10¹⁰⁰(101-digit number)

25206710870907166910…63423663698993479681

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

5.041 × 10¹⁰⁰(101-digit number)

50413421741814333820…26847327397986959359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.041 × 10¹⁰⁰(101-digit number)

50413421741814333820…26847327397986959361

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 #673,834

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