Block #1,091,922

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/6/2015, 6:32:05 AM · Difficulty 10.7380 · 5,718,934 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

248175b89c6ad5d0e1c2568df0237bdbcf482335d1c615771664f70fcfb39b7c

View on Chainz ↗

Height

#1,091,922

Difficulty

10.737999

Transactions

Size

202 B

Version

Bits

0abced80

Nonce

36,371,287

Timestamp

6/6/2015, 6:32:05 AM

Confirmations

5,718,934

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

65c4221b44a1d369177873865d153e296c0d31d40769f740647d78e70e6092f7

Transactions (1)

Coinbase65c4221b44a1d3…7d78e70e6092f7

1 in → 1 out8.6600 XPM109 B

ANCZAhFA…4XJ8NSvi

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.

5.481 × 10¹⁰⁰(101-digit number)

54818009293369070231…88838700237327564799

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

5.481 × 10¹⁰⁰(101-digit number)

54818009293369070231…88838700237327564799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.481 × 10¹⁰⁰(101-digit number)

54818009293369070231…88838700237327564801

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

1.096 × 10¹⁰¹(102-digit number)

10963601858673814046…77677400474655129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.096 × 10¹⁰¹(102-digit number)

10963601858673814046…77677400474655129601

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

2.192 × 10¹⁰¹(102-digit number)

21927203717347628092…55354800949310259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.192 × 10¹⁰¹(102-digit number)

21927203717347628092…55354800949310259201

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

4.385 × 10¹⁰¹(102-digit number)

43854407434695256185…10709601898620518399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.385 × 10¹⁰¹(102-digit number)

43854407434695256185…10709601898620518401

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

8.770 × 10¹⁰¹(102-digit number)

87708814869390512370…21419203797241036799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.770 × 10¹⁰¹(102-digit number)

87708814869390512370…21419203797241036801

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 #1,091,922

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