Block #427,130

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 4:23:52 AM · Difficulty 10.3463 · 6,374,401 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

773e6e4a99ade5e773cb7dc8cd5a78913a8105ff1ca393f496746f4c46b4747a

View on Chainz ↗

Height

#427,130

Difficulty

10.346316

Transactions

Size

1.02 KB

Version

Bits

0a58a82b

Nonce

1,020,245

Timestamp

3/3/2014, 4:23:52 AM

Confirmations

6,374,401

Mined by

⛏️ zaSaAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ec5bf115452530836b16324cf935f9888c3c9c4bcacf4561c549cab5b038521c

Transactions (1)

Coinbaseec5bf115452530…49cab5b038521c

1 in → 26 out9.3300 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

8.800 × 10¹⁰⁰(101-digit number)

88008505295559131507…99181117177360629759

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

8.800 × 10¹⁰⁰(101-digit number)

88008505295559131507…99181117177360629759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.800 × 10¹⁰⁰(101-digit number)

88008505295559131507…99181117177360629761

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

1.760 × 10¹⁰¹(102-digit number)

17601701059111826301…98362234354721259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.760 × 10¹⁰¹(102-digit number)

17601701059111826301…98362234354721259521

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

3.520 × 10¹⁰¹(102-digit number)

35203402118223652602…96724468709442519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.520 × 10¹⁰¹(102-digit number)

35203402118223652602…96724468709442519041

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

7.040 × 10¹⁰¹(102-digit number)

70406804236447305205…93448937418885038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.040 × 10¹⁰¹(102-digit number)

70406804236447305205…93448937418885038081

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

1.408 × 10¹⁰²(103-digit number)

14081360847289461041…86897874837770076159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.408 × 10¹⁰²(103-digit number)

14081360847289461041…86897874837770076161

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