Block #2,291,571

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2017, 4:27:25 AM · Difficulty 10.9550 · 4,541,695 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f17f9063a2b1add8e91cd2cbb0e77c02380d2a56359835e7207194ec0c45baab

View on Chainz ↗

Height

#2,291,571

Difficulty

10.954977

Transactions

Size

879 B

Version

Bits

0af4795b

Nonce

295,881,410

Timestamp

9/11/2017, 4:27:25 AM

Confirmations

4,541,695

Mined by

⛏️ P2SHAQGK33pz1PMfM5nsiKXpGL9P49TeVPVLR1

Merkle Root

74b6f592e86f43320b6f2128342b78e776a383baef13d12db8c6e05edf616d92

Transactions (4)

Coinbasef3965893a6a77d…b2ddda39607361

1 in → 1 out8.3500 XPM110 B

AQGK33pz…TeVPVLR1

0af658c968c4c4…a27e080c00fc1a

1 in → 2 out9207.6524 XPM227 B

Ac9XWHWc…KtPkq8rd AdQXAVzV…Porr8zSX

1d48e792c87c6c…ce40434efa6ebf

1 in → 2 out9164.5892 XPM226 B

AcwpivWD…mierTCnU AVdyLdio…xcPHqVti

4821340a9fa869…a09a8da87b0100

1 in → 2 out1892.8444 XPM226 B

AVdyLdio…xcPHqVti AcuzzLfj…XZYWWM6Z

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.

6.235 × 10⁹³(94-digit number)

62353988249825546011…04267699694227052319

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

6.235 × 10⁹³(94-digit number)

62353988249825546011…04267699694227052319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.235 × 10⁹³(94-digit number)

62353988249825546011…04267699694227052321

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

1.247 × 10⁹⁴(95-digit number)

12470797649965109202…08535399388454104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.247 × 10⁹⁴(95-digit number)

12470797649965109202…08535399388454104641

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

2.494 × 10⁹⁴(95-digit number)

24941595299930218404…17070798776908209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.494 × 10⁹⁴(95-digit number)

24941595299930218404…17070798776908209281

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

4.988 × 10⁹⁴(95-digit number)

49883190599860436809…34141597553816418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.988 × 10⁹⁴(95-digit number)

49883190599860436809…34141597553816418561

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

9.976 × 10⁹⁴(95-digit number)

99766381199720873618…68283195107632837119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.976 × 10⁹⁴(95-digit number)

99766381199720873618…68283195107632837121

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 #2,291,571

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