Block #430,599

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 2:37:48 PM · Difficulty 10.3455 · 6,386,343 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

796cf437400380515c7eb6229e08e67ea190dbc5ebcaab90043f9821d5804a98

View on Chainz ↗

Height

#430,599

Difficulty

10.345500

Transactions

Size

1.75 KB

Version

Bits

0a5872a9

Nonce

217,875

Timestamp

3/5/2014, 2:37:48 PM

Confirmations

6,386,343

Mined by

⛏️ P2SHAXUg74qDidwHuXKxiXX8fTn1tgdrvRRqLX

Merkle Root

b7c220282aaf90587096604a9d2a709f34f7591a2f94cebb5b29d575abc9b31f

Transactions (5)

Coinbase7f4a535faba626…b2fd94f1f096a5

1 in → 1 out9.3700 XPM109 B

AXUg74qD…drvRRqLX

be22b0865bbd17…c36d49cecfcb9d

4 in → 13 out37.3800 XPM907 B

AYCUUvNh…VhSPTgYs AUkLzhdx…6FJGTCiB ALxaSzoH…c8tfqwKi AKxMtejp…1A9Q7AU5 ALMhWeDo…UZNXqBtr

6661b5644eaa3f…1e4c0e838a78f8

1 in → 2 out4860.1474 XPM226 B

APRWSjBU…A24rJqGA AGfKfQZf…phYQjYF3

9f18a2de91f55c…dbbcfa3806bb0b

1 in → 2 out136.7544 XPM226 B

AKSxfKfu…PrY2y58U Ab1YyXQ8…tUHUC2fG

5b86f9a9eb05a3…6d608dc27b631f

1 in → 2 out135.7444 XPM226 B

AKSxfKfu…PrY2y58U ATt6xAop…29qTKt6V

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.

4.729 × 10¹⁰⁰(101-digit number)

47294375288529895198…82077143492277288959

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

4.729 × 10¹⁰⁰(101-digit number)

47294375288529895198…82077143492277288959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.729 × 10¹⁰⁰(101-digit number)

47294375288529895198…82077143492277288961

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

9.458 × 10¹⁰⁰(101-digit number)

94588750577059790396…64154286984554577919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.458 × 10¹⁰⁰(101-digit number)

94588750577059790396…64154286984554577921

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

1.891 × 10¹⁰¹(102-digit number)

18917750115411958079…28308573969109155839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.891 × 10¹⁰¹(102-digit number)

18917750115411958079…28308573969109155841

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

3.783 × 10¹⁰¹(102-digit number)

37835500230823916158…56617147938218311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.783 × 10¹⁰¹(102-digit number)

37835500230823916158…56617147938218311681

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

7.567 × 10¹⁰¹(102-digit number)

75671000461647832317…13234295876436623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.567 × 10¹⁰¹(102-digit number)

75671000461647832317…13234295876436623361

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 #430,599

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