Block #430,044

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 6:03:53 AM · Difficulty 10.3400 · 6,382,080 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ced406f43f21103833aebf2c6c70b8dda8be71445035a0d53c4721d450a48cb7

View on Chainz ↗

Height

#430,044

Difficulty

10.339952

Transactions

Size

834 B

Version

Bits

0a57071e

Nonce

12,474

Timestamp

3/5/2014, 6:03:53 AM

Confirmations

6,382,080

Mined by

⛏️ aS@AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

327d15b6c51ff3f894197fb574578bafb4c0fe7d9c9d805cd13a4bd4b89927aa

Transactions (1)

Coinbase327d15b6c51ff3…3a4bd4b89927aa

1 in → 20 out9.3400 XPM743 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.

6.226 × 10⁹⁶(97-digit number)

62267879776993084738…50615258995444438129

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

6.226 × 10⁹⁶(97-digit number)

62267879776993084738…50615258995444438129

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.226 × 10⁹⁶(97-digit number)

62267879776993084738…50615258995444438131

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

1.245 × 10⁹⁷(98-digit number)

12453575955398616947…01230517990888876259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.245 × 10⁹⁷(98-digit number)

12453575955398616947…01230517990888876261

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

2.490 × 10⁹⁷(98-digit number)

24907151910797233895…02461035981777752519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.490 × 10⁹⁷(98-digit number)

24907151910797233895…02461035981777752521

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

4.981 × 10⁹⁷(98-digit number)

49814303821594467790…04922071963555505039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.981 × 10⁹⁷(98-digit number)

49814303821594467790…04922071963555505041

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

9.962 × 10⁹⁷(98-digit number)

99628607643188935581…09844143927111010079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.962 × 10⁹⁷(98-digit number)

99628607643188935581…09844143927111010081

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 #430,044

Cookie Preferences