Block #360,711

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 2:53:31 PM · Difficulty 10.3979 · 6,449,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3af2249615c9d25f887601fa7b12f46bebe538404ebcb9919c4936f74dab370f

View on Chainz ↗

Height

#360,711

Difficulty

10.397926

Transactions

Size

697 B

Version

Bits

0a65de79

Nonce

8,219

Timestamp

1/15/2014, 2:53:31 PM

Confirmations

6,449,255

Mined by

AFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

59fc897c7918d814b8e98efa487b0891d6fa464cde752e100002993d2e0a5fe6

Transactions (1)

Coinbase59fc897c7918d8…02993d2e0a5fe6

1 in → 16 out9.2400 XPM607 B

AFutDVqJ…TJTJj6UF AMHMrUuK…jgEj6HLr AShKwBPr…M993r1eU AczyTBWn…bEQQj33u AGAqbmge…Htpnvw1k

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.

2.511 × 10⁹⁵(96-digit number)

25111830795656865114…74282112760178283519

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

2.511 × 10⁹⁵(96-digit number)

25111830795656865114…74282112760178283519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.511 × 10⁹⁵(96-digit number)

25111830795656865114…74282112760178283521

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

5.022 × 10⁹⁵(96-digit number)

50223661591313730228…48564225520356567039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.022 × 10⁹⁵(96-digit number)

50223661591313730228…48564225520356567041

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

1.004 × 10⁹⁶(97-digit number)

10044732318262746045…97128451040713134079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁶(97-digit number)

10044732318262746045…97128451040713134081

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

2.008 × 10⁹⁶(97-digit number)

20089464636525492091…94256902081426268159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.008 × 10⁹⁶(97-digit number)

20089464636525492091…94256902081426268161

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

4.017 × 10⁹⁶(97-digit number)

40178929273050984183…88513804162852536319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.017 × 10⁹⁶(97-digit number)

40178929273050984183…88513804162852536321

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 #360,711

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