Block #521,773

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2014, 4:10:44 PM · Difficulty 10.8636 · 6,276,350 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bad2022146bad001fe0055053c1045e7972ff3007b3c1608066084f3dfcc73d7

View on Chainz ↗

Height

#521,773

Difficulty

10.863613

Transactions

Size

660 B

Version

Bits

0add15c6

Nonce

9,851,406

Timestamp

5/2/2014, 4:10:44 PM

Confirmations

6,276,350

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fa43a77ba33cade5782fdf94bbeffe5fe6cb70c2306bfdf6d0b98d5551a66c6e

Transactions (3)

Coinbase86abfd220dbeab…36862f703cb2dd

1 in → 1 out8.4800 XPM116 B

AbwWkWZt…kawDhufa

bd17b65ea645e8…3a1e6c560cd2e6

1 in → 2 out7.4587 XPM225 B

APfH1y47…dxXKNM9L AaTADdiV…iYKavcmf

f5129fc332242b…733abb5b67ea65

1 in → 2 out6.4188 XPM227 B

AJmepCtW…qaAda9vP AWr7QESV…T91HodnJ

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.

4.094 × 10⁹⁸(99-digit number)

40946187549940318053…40913550699069339039

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

4.094 × 10⁹⁸(99-digit number)

40946187549940318053…40913550699069339039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.094 × 10⁹⁸(99-digit number)

40946187549940318053…40913550699069339041

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

8.189 × 10⁹⁸(99-digit number)

81892375099880636107…81827101398138678079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.189 × 10⁹⁸(99-digit number)

81892375099880636107…81827101398138678081

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

1.637 × 10⁹⁹(100-digit number)

16378475019976127221…63654202796277356159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.637 × 10⁹⁹(100-digit number)

16378475019976127221…63654202796277356161

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

3.275 × 10⁹⁹(100-digit number)

32756950039952254442…27308405592554712319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.275 × 10⁹⁹(100-digit number)

32756950039952254442…27308405592554712321

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

6.551 × 10⁹⁹(100-digit number)

65513900079904508885…54616811185109424639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.551 × 10⁹⁹(100-digit number)

65513900079904508885…54616811185109424641

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