Block #726,170

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/17/2014, 6:14:17 PM · Difficulty 10.9608 · 6,083,465 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f2a2cd39a2859a0c985de273e0667f4cdbd076398e4ac66dfd8b695bc305569

View on Chainz ↗

Height

#726,170

Difficulty

10.960810

Transactions

Size

796 B

Version

Bits

0af5f7a3

Nonce

1,602,024,239

Timestamp

9/17/2014, 6:14:17 PM

Confirmations

6,083,465

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

022b4f3f7dee7bbd567dc19dab641bff91774d105dfbb683861ace5cbe081c49

Transactions (3)

Coinbase829bd8a1e1e201…69944c72018144

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

6fba8e32cad86c…054f3bf6e5f14b

1 in → 6 out8.3000 XPM361 B

AJRwGPSP…QDRWdi2B AaVFHFSq…bCnX1Bpw Acv4s4hy…q1NdRHK1 AcGtRvwd…TB9o7tUF AckrQkQZ…bZLQ2nG1

daa8fa201dc746…4dad7113b4831e

1 in → 2 out1.3761 XPM227 B

AHGYdLMi…rgVqzAmf Abs1CTRR…uk6ieBYF

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.

2.212 × 10⁹⁹(100-digit number)

22123644841972619191…89390315330919137279

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

2.212 × 10⁹⁹(100-digit number)

22123644841972619191…89390315330919137279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.212 × 10⁹⁹(100-digit number)

22123644841972619191…89390315330919137281

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

4.424 × 10⁹⁹(100-digit number)

44247289683945238382…78780630661838274559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.424 × 10⁹⁹(100-digit number)

44247289683945238382…78780630661838274561

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

8.849 × 10⁹⁹(100-digit number)

88494579367890476764…57561261323676549119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.849 × 10⁹⁹(100-digit number)

88494579367890476764…57561261323676549121

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

1.769 × 10¹⁰⁰(101-digit number)

17698915873578095352…15122522647353098239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.769 × 10¹⁰⁰(101-digit number)

17698915873578095352…15122522647353098241

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

3.539 × 10¹⁰⁰(101-digit number)

35397831747156190705…30245045294706196479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.539 × 10¹⁰⁰(101-digit number)

35397831747156190705…30245045294706196481

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 #726,170

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