Block #429,028

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 12:25:47 PM · Difficulty 10.3446 · 6,387,685 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9ec420fefb0b8a074c379e390238f855a245c549218e7afa1c855c86b7bc495

View on Chainz ↗

Height

#429,028

Difficulty

10.344620

Transactions

Size

1.30 KB

Version

Bits

0a583902

Nonce

233,018

Timestamp

3/4/2014, 12:25:47 PM

Confirmations

6,387,685

Mined by

⛏️ P2SHAQo5Sf84DcjUC65gbiaUvY1LDSCktZTnkR

Merkle Root

041eaf6ee9f90e402784e3e3468f337177d41d0bae6ecad83ca40d298251d0fe

Transactions (2)

Coinbaseb8097b51a76387…e1b548525a1816

1 in → 1 out9.3500 XPM109 B

AQo5Sf84…CktZTnkR

0c971f45692a0f…f6fd45ae9169af

6 in → 10 out29.2448 XPM1.11 KB

AdSXFDPP…ANJyvdi7 AT17PSFn…faxELw2p AeKNrjNj…1NEq95Ta AdYH33yX…NKufJznD AP4MPyKc…JbZeSack

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.

9.011 × 10⁹²(93-digit number)

90112676027134256892…42234298737633471039

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

9.011 × 10⁹²(93-digit number)

90112676027134256892…42234298737633471039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.011 × 10⁹²(93-digit number)

90112676027134256892…42234298737633471041

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

1.802 × 10⁹³(94-digit number)

18022535205426851378…84468597475266942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.802 × 10⁹³(94-digit number)

18022535205426851378…84468597475266942081

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

3.604 × 10⁹³(94-digit number)

36045070410853702756…68937194950533884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.604 × 10⁹³(94-digit number)

36045070410853702756…68937194950533884161

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

7.209 × 10⁹³(94-digit number)

72090140821707405513…37874389901067768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.209 × 10⁹³(94-digit number)

72090140821707405513…37874389901067768321

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

1.441 × 10⁹⁴(95-digit number)

14418028164341481102…75748779802135536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.441 × 10⁹⁴(95-digit number)

14418028164341481102…75748779802135536641

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 #429,028

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