Block #193,960

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 8:15:24 PM · Difficulty 9.8780 · 6,623,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

baa18a8a91dc7788302c038a0e98d4376ae380bbf758f42a6e2ba27cb75c5bee

View on Chainz ↗

Height

#193,960

Difficulty

9.878010

Transactions

Size

2.55 KB

Version

Bits

09e0c53d

Nonce

83,100

Timestamp

10/4/2013, 8:15:24 PM

Confirmations

6,623,398

Mined by

⛏️ P2SHAWKLbdikDJBNwg6tqhSF566ybZA4VMuxRe

Merkle Root

76a44154817ab4d626dfd0722c66f95a14563fb4fb75f1b199967f94bc6291d3

Transactions (4)

Coinbase7deb9a6460dc58…e439ebf0386cba

1 in → 1 out10.2700 XPM109 B

AWKLbdik…A4VMuxRe

1abbc2a35b2ec0…22593bd3e164ae

11 in → 2 out103.0300 XPM1.34 KB

AQAvQSWZ…C9mFkvux ANuiNC3L…vDawLmGV

92158290b9130f…12af8617073ed3

5 in → 2 out51.1900 XPM818 B

ANP3mT5K…dkjrtVpK AJFedaG6…jXUaiPL2

b25ce692bbd9aa…d5c5cc82324c24

1 in → 2 out2.0329 XPM225 B

AeYsF2qq…KmffVGCm AeMmfENn…jNrRQskV

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.

8.942 × 10¹⁰²(103-digit number)

89420089376666630275…63508102449088266239

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

8.942 × 10¹⁰²(103-digit number)

89420089376666630275…63508102449088266239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.942 × 10¹⁰²(103-digit number)

89420089376666630275…63508102449088266241

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

1.788 × 10¹⁰³(104-digit number)

17884017875333326055…27016204898176532479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.788 × 10¹⁰³(104-digit number)

17884017875333326055…27016204898176532481

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

3.576 × 10¹⁰³(104-digit number)

35768035750666652110…54032409796353064959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.576 × 10¹⁰³(104-digit number)

35768035750666652110…54032409796353064961

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

7.153 × 10¹⁰³(104-digit number)

71536071501333304220…08064819592706129919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.153 × 10¹⁰³(104-digit number)

71536071501333304220…08064819592706129921

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

1.430 × 10¹⁰⁴(105-digit number)

14307214300266660844…16129639185412259839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #193,960

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