Block #429,570

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 9:16:28 PM · Difficulty 10.3464 · 6,386,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

362b847960e3afa2db98b1b3dab3b5f8b28137896e785d8dae8a43adf4f87898

View on Chainz ↗

Height

#429,570

Difficulty

10.346373

Transactions

Size

1.06 KB

Version

Bits

0a58abeb

Nonce

42,096

Timestamp

3/4/2014, 9:16:28 PM

Confirmations

6,386,928

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f753f465795fe3ffbda5b32922c663aaea0b6550ac80ed36c51cccd600fde243

Transactions (2)

Coinbaseea323a2cf2ed0f…5cfdef464e2d61

1 in → 1 out9.3400 XPM116 B

AbwWkWZt…kawDhufa

82198e77f9e54c…b07aed14bc8e8b

4 in → 12 out37.2600 XPM873 B

AahpcZUi…qkuqDHbZ AZfJBbCQ…7AystqGz AUHFmvnF…juaRoiLd ALG6Kwki…JVRCDqef AVy7vA87…WkzNt12Y

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.

1.429 × 10¹⁰¹(102-digit number)

14299712007244295798…19723064193155251199

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

1.429 × 10¹⁰¹(102-digit number)

14299712007244295798…19723064193155251199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.429 × 10¹⁰¹(102-digit number)

14299712007244295798…19723064193155251201

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

2.859 × 10¹⁰¹(102-digit number)

28599424014488591596…39446128386310502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.859 × 10¹⁰¹(102-digit number)

28599424014488591596…39446128386310502401

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

5.719 × 10¹⁰¹(102-digit number)

57198848028977183192…78892256772621004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.719 × 10¹⁰¹(102-digit number)

57198848028977183192…78892256772621004801

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

1.143 × 10¹⁰²(103-digit number)

11439769605795436638…57784513545242009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.143 × 10¹⁰²(103-digit number)

11439769605795436638…57784513545242009601

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

2.287 × 10¹⁰²(103-digit number)

22879539211590873277…15569027090484019199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.287 × 10¹⁰²(103-digit number)

22879539211590873277…15569027090484019201

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 #429,570

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