Block #284,315

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 2:12:12 AM · Difficulty 9.9825 · 6,526,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

845de9768246c3b19264771525eda5fcbe89d8dbf360868345ab5539a6b6b9de

View on Chainz ↗

Height

#284,315

Difficulty

9.982501

Transactions

Size

2.79 KB

Version

Bits

09fb8528

Nonce

166,299

Timestamp

11/30/2013, 2:12:12 AM

Confirmations

6,526,758

Mined by

⛏️ VaRIs0AKde1i4dpqpgDtEArAY3oRXX8K88R1bw6g

Merkle Root

9be0718d3fd4574490d36900669f283deb3a10f977d9516162521622aabdd23c

Transactions (4)

Coinbasefaefba23e36f7c…08ddb79721b734

1 in → 29 out10.0000 XPM1.02 KB

AKde1i4d…88R1bw6g AJ9QW1VP…GmAJhvhc AWGQhzDN…RDYvugUy AYckRkCF…TgDe5VSp AahbzMCB…mFJF5Kys

2c13c2c78f8cc2…6a8dac9cc68949

8 in → 2 out8.0100 XPM1.23 KB

ANcKNSXM…Vd5xbiKY AUkzF5wJ…kGWBLQHp

2af77bc44680cf…d4c995ae38206e

1 in → 2 out6.9062 XPM226 B

AaVNPKxe…Bm9pCDPj AWhqddAm…5ggySXwy

5d7891b47f3b5b…52779abc906cb5

1 in → 2 out5.8789 XPM225 B

AHsxJBCr…VeUUr8q8 AGdRGBi6…B5NBHeS9

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.

9.046 × 10⁹³(94-digit number)

90462553250095264184…96431273253845699839

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

9.046 × 10⁹³(94-digit number)

90462553250095264184…96431273253845699839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.046 × 10⁹³(94-digit number)

90462553250095264184…96431273253845699841

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

1.809 × 10⁹⁴(95-digit number)

18092510650019052836…92862546507691399679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.809 × 10⁹⁴(95-digit number)

18092510650019052836…92862546507691399681

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

3.618 × 10⁹⁴(95-digit number)

36185021300038105673…85725093015382799359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.618 × 10⁹⁴(95-digit number)

36185021300038105673…85725093015382799361

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

7.237 × 10⁹⁴(95-digit number)

72370042600076211347…71450186030765598719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.237 × 10⁹⁴(95-digit number)

72370042600076211347…71450186030765598721

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

1.447 × 10⁹⁵(96-digit number)

14474008520015242269…42900372061531197439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.447 × 10⁹⁵(96-digit number)

14474008520015242269…42900372061531197441

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 #284,315

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