Block #1,109,140

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/16/2015, 5:40:24 AM · Difficulty 10.8521 · 5,703,694 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

182bfe5c7f5b22132b37d56b7ee814717c90b3e754ffe57fbcf410df0704b8f0

View on Chainz ↗

Height

#1,109,140

Difficulty

10.852107

Transactions

Size

3.20 KB

Version

Bits

0ada23aa

Nonce

266,841,242

Timestamp

6/16/2015, 5:40:24 AM

Confirmations

5,703,694

Mined by

⛏️ P2SHAWP9YkdvtGSMqBsiRnjYMdK8NtCav3LhV9

Merkle Root

5531d00b9bfd66e4aa3b1b7bad2568244cda4e99ff18e179ba107dc7a5adeb48

Transactions (3)

Coinbase4dbf135eb194ba…fcdd4605998767

1 in → 1 out8.5300 XPM110 B

AWP9Ykdv…Cav3LhV9

1a674ef4807c94…915c8a9f245a62

10 in → 1 out46.6233 XPM1.49 KB

ARoPpPjC…Ndoa3iQv

73dae966f8b176…b171683cd9af1f

10 in → 2 out32.9288 XPM1.52 KB

AJdM6BQD…g1g59wty APmEZykM…ao1DNrhH

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.

9.059 × 10⁹⁴(95-digit number)

90596313229081326718…22214293657424683999

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

9.059 × 10⁹⁴(95-digit number)

90596313229081326718…22214293657424683999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.059 × 10⁹⁴(95-digit number)

90596313229081326718…22214293657424684001

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

1.811 × 10⁹⁵(96-digit number)

18119262645816265343…44428587314849367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.811 × 10⁹⁵(96-digit number)

18119262645816265343…44428587314849368001

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

3.623 × 10⁹⁵(96-digit number)

36238525291632530687…88857174629698735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.623 × 10⁹⁵(96-digit number)

36238525291632530687…88857174629698736001

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

7.247 × 10⁹⁵(96-digit number)

72477050583265061374…77714349259397471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.247 × 10⁹⁵(96-digit number)

72477050583265061374…77714349259397472001

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

1.449 × 10⁹⁶(97-digit number)

14495410116653012274…55428698518794943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.449 × 10⁹⁶(97-digit number)

14495410116653012274…55428698518794944001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.899 × 10⁹⁶(97-digit number)

28990820233306024549…10857397037589887999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,109,140

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