Block #1,105,075

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2015, 8:20:19 PM · Difficulty 10.7770 · 5,737,235 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96b3b49516d61b84cb60a1c1d345d08a0c562267fe297475f6533859869188f2

View on Chainz ↗

Height

#1,105,075

Difficulty

10.777048

Transactions

Size

1.14 KB

Version

Bits

0ac6ec9f

Nonce

345,482,801

Timestamp

6/14/2015, 8:20:19 PM

Confirmations

5,737,235

Mined by

⛏️ P2SHAVpZcHgBBdyPgXDLr8Zv6NCGMSnbeHjK1N

Merkle Root

2b6917f8473da5ae647d4d60a5042ab02047f5493a5bec4887d729634800571c

Transactions (2)

Coinbase217fb3fc25579f…674c92dcf7738a

1 in → 1 out8.6100 XPM110 B

AVpZcHgB…nbeHjK1N

5982ace2e55998…ca7ce6287af217

6 in → 2 out119.3965 XPM964 B

AMV1f87g…ebBHKibX ALRuXegM…qhkfJpvU

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.

2.297 × 10⁹⁶(97-digit number)

22979081129911558551…88224169729826355199

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

2.297 × 10⁹⁶(97-digit number)

22979081129911558551…88224169729826355199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.297 × 10⁹⁶(97-digit number)

22979081129911558551…88224169729826355201

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

4.595 × 10⁹⁶(97-digit number)

45958162259823117103…76448339459652710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.595 × 10⁹⁶(97-digit number)

45958162259823117103…76448339459652710401

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

9.191 × 10⁹⁶(97-digit number)

91916324519646234206…52896678919305420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.191 × 10⁹⁶(97-digit number)

91916324519646234206…52896678919305420801

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

1.838 × 10⁹⁷(98-digit number)

18383264903929246841…05793357838610841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.838 × 10⁹⁷(98-digit number)

18383264903929246841…05793357838610841601

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

3.676 × 10⁹⁷(98-digit number)

36766529807858493682…11586715677221683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.676 × 10⁹⁷(98-digit number)

36766529807858493682…11586715677221683201

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 #1,105,075

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