Block #285,005

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 8:23:19 AM · Difficulty 9.9836 · 6,539,678 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

136992ad20517d91e9c17994165ab24e9b0229cce909757873115d2c4834cf24

View on Chainz ↗

Height

#285,005

Difficulty

9.983601

Transactions

Size

845 B

Version

Bits

09fbcd41

Nonce

6,317

Timestamp

11/30/2013, 8:23:19 AM

Confirmations

6,539,678

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

02f35a2dd3b674f52bba1830b8d3b641e3844100898b1b89fb5ff7333a442165

Transactions (4)

Coinbase68c892d8aa6a19…2605c7c6078e72

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

0986592515ec2c…dc279327380113

1 in → 2 out20437.2569 XPM226 B

AYDojcZy…ymHLjnTx APXDbZkV…XN95Snst

2b09a89a4a65cb…550105bd498af2

1 in → 2 out1.5991 XPM226 B

AVEmWzX6…ZugFLj5v APwxw58r…Gak69sM3

60f990c12a22d0…15ab1ad3455861

1 in → 1 out0.2912 XPM192 B

AJH4pYyW…97uF2Gbn

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.

3.264 × 10⁹⁶(97-digit number)

32645668891374667481…28646608120895375679

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

3.264 × 10⁹⁶(97-digit number)

32645668891374667481…28646608120895375679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.264 × 10⁹⁶(97-digit number)

32645668891374667481…28646608120895375681

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

6.529 × 10⁹⁶(97-digit number)

65291337782749334963…57293216241790751359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.529 × 10⁹⁶(97-digit number)

65291337782749334963…57293216241790751361

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

1.305 × 10⁹⁷(98-digit number)

13058267556549866992…14586432483581502719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.305 × 10⁹⁷(98-digit number)

13058267556549866992…14586432483581502721

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

2.611 × 10⁹⁷(98-digit number)

26116535113099733985…29172864967163005439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.611 × 10⁹⁷(98-digit number)

26116535113099733985…29172864967163005441

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

5.223 × 10⁹⁷(98-digit number)

52233070226199467970…58345729934326010879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.223 × 10⁹⁷(98-digit number)

52233070226199467970…58345729934326010881

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 #285,005

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