Block #285,474

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 12:26:46 PM · Difficulty 9.9843 · 6,510,957 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81922f1221451ccf9c66b1efa541099645049a400dcc220c0e99da75e479a4ac

View on Chainz ↗

Height

#285,474

Difficulty

9.984330

Transactions

Size

4.39 KB

Version

Bits

09fbfd0e

Nonce

40,506

Timestamp

11/30/2013, 12:26:46 PM

Confirmations

6,510,957

Mined by

APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

67710142600ad487b1d24efc6e7d39d1b06f2ba4cdfddafc2481f2e8694b1889

Transactions (4)

Coinbase145e38abdc61c0…6c70112fdab9ca

1 in → 25 out10.0200 XPM912 B

APeshfYV…3PKcKMKH AGFAJ5YL…ZEnBbk6G Ad9pSzHt…cpJ3y2zz AKde1i4d…88R1bw6g ANkX1YyE…kHwVW1hd

a4c8449ec41841…f80fad4a5387b9

2 in → 2 out56.1266 XPM373 B

AH4WnBzi…CzV3NQi6 AcK2HALC…YEooUj8S

0f180d539912ce…fa52c9f697553f

19 in → 2 out200.1231 XPM2.82 KB

AUht9CPU…ECEJbPQ8 AJsoQMih…2D7KoAZ1

bc4969f8237144…065d19d77d1aa5

1 in → 2 out2.8433 XPM227 B

AcuGVeNL…6i4Gp26k AL7z4J47…ySw6Jp45

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.

5.872 × 10⁹³(94-digit number)

58720421687946886559…36180448337978519359

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

5.872 × 10⁹³(94-digit number)

58720421687946886559…36180448337978519359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.872 × 10⁹³(94-digit number)

58720421687946886559…36180448337978519361

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

1.174 × 10⁹⁴(95-digit number)

11744084337589377311…72360896675957038719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.174 × 10⁹⁴(95-digit number)

11744084337589377311…72360896675957038721

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

2.348 × 10⁹⁴(95-digit number)

23488168675178754623…44721793351914077439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.348 × 10⁹⁴(95-digit number)

23488168675178754623…44721793351914077441

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

4.697 × 10⁹⁴(95-digit number)

46976337350357509247…89443586703828154879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.697 × 10⁹⁴(95-digit number)

46976337350357509247…89443586703828154881

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

9.395 × 10⁹⁴(95-digit number)

93952674700715018495…78887173407656309759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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