Block #1,110,036

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/16/2015, 12:26:46 PM · Difficulty 10.8658 · 5,696,558 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d62db0d58eca7cf268aa07871eec017d547a0e62d32d2769d61b2b916b5d3847

View on Chainz ↗

Height

#1,110,036

Difficulty

10.865826

Transactions

Size

9.90 KB

Version

Bits

0adda6c1

Nonce

813,190,887

Timestamp

6/16/2015, 12:26:46 PM

Confirmations

5,696,558

Mined by

⛏️ P2SHAeN5eEMrnMRvwTALSGCRBpLcKcbWQw5ka2

Merkle Root

c48e7078adfd62a44096546fb800b54fe6ef8513e08fc651a80ee10f3a5f44d2

Transactions (2)

Coinbase12ea5189d01b4f…6a97dd668af63a

1 in → 1 out8.5600 XPM110 B

AeN5eEMr…bWQw5ka2

ac4027e8cd4ace…98433525b3f78a

72 in → 2 out211.0112 XPM9.71 KB

AWwRuEjj…PFr4pRJq ARWv5fnJ…TKKV2NWQ

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.

1.700 × 10⁹³(94-digit number)

17000082491142867023…96780311693865136879

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

1.700 × 10⁹³(94-digit number)

17000082491142867023…96780311693865136879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.700 × 10⁹³(94-digit number)

17000082491142867023…96780311693865136881

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

3.400 × 10⁹³(94-digit number)

34000164982285734047…93560623387730273759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.400 × 10⁹³(94-digit number)

34000164982285734047…93560623387730273761

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

6.800 × 10⁹³(94-digit number)

68000329964571468095…87121246775460547519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.800 × 10⁹³(94-digit number)

68000329964571468095…87121246775460547521

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

1.360 × 10⁹⁴(95-digit number)

13600065992914293619…74242493550921095039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.360 × 10⁹⁴(95-digit number)

13600065992914293619…74242493550921095041

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

2.720 × 10⁹⁴(95-digit number)

27200131985828587238…48484987101842190079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.720 × 10⁹⁴(95-digit number)

27200131985828587238…48484987101842190081

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 #1,110,036

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