Block #520,014

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2014, 2:33:10 PM · Difficulty 10.8575 · 6,286,874 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3122947da0c265cde813fda7a8586af7283189304a8248a7c682bf58f887ae9

View on Chainz ↗

Height

#520,014

Difficulty

10.857484

Transactions

Size

29.28 KB

Version

Bits

0adb841a

Nonce

17,944

Timestamp

5/1/2014, 2:33:10 PM

Confirmations

6,286,874

Mined by

⛏️ NAKUN1D7mcA4QwLGNyRvGmKSfchyVvTNUMM

Merkle Root

9d8d98729a6fac1db3e0b34e1eb6558e6707576d66c360b4509d3bf792f71c00

Transactions (5)

Coinbaseb03a592370b19e…b918c802fc1286

1 in → 2 out8.8000 XPM131 B

AKUN1D7m…yVvTNUMM AcaoBAGZ…n7zfVgjk

416bd1ce2fc7ba…c09b340b662dbf

1 in → 2 out8.4700 XPM226 B

AewGasuv…7CEsmomB ANj5CH87…dbHEWtVC

a2ebd9b66ddce3…7f229099b0a333

196 in → 2 out500.0100 XPM28.40 KB

AJjnK9uC…VreFquR4 AG7JwctS…CsK59x2c

fbe6edbda6038d…e49ff5bf7befb9

1 in → 2 out5.8805 XPM226 B

AS1H11SD…W6QcaUb8 AULkviz4…6ZwMzqc9

ce90ceb822ff06…f6cb530d30737e

1 in → 2 out4.3787 XPM226 B

AaQokYRw…WhXNDda4 AaddUcpX…Spoua76E

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.

4.017 × 10¹⁰¹(102-digit number)

40179717555088374286…37098252371180076159

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

4.017 × 10¹⁰¹(102-digit number)

40179717555088374286…37098252371180076159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.017 × 10¹⁰¹(102-digit number)

40179717555088374286…37098252371180076161

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

8.035 × 10¹⁰¹(102-digit number)

80359435110176748573…74196504742360152319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.035 × 10¹⁰¹(102-digit number)

80359435110176748573…74196504742360152321

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

1.607 × 10¹⁰²(103-digit number)

16071887022035349714…48393009484720304639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.607 × 10¹⁰²(103-digit number)

16071887022035349714…48393009484720304641

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

3.214 × 10¹⁰²(103-digit number)

32143774044070699429…96786018969440609279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.214 × 10¹⁰²(103-digit number)

32143774044070699429…96786018969440609281

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

6.428 × 10¹⁰²(103-digit number)

64287548088141398858…93572037938881218559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.428 × 10¹⁰²(103-digit number)

64287548088141398858…93572037938881218561

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 #520,014

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