Block #89,575

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 11:32:18 AM · Difficulty 9.2563 · 6,737,560 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09bf2ef71435fb9b12fd29bf75937117f617bae9a2b393fc777ee926b75af8d8

View on Chainz ↗

Height

#89,575

Difficulty

9.256326

Transactions

Size

808 B

Version

Bits

09419e98

Nonce

40,120

Timestamp

7/30/2013, 11:32:18 AM

Confirmations

6,737,560

Mined by

⛏️ P2SHAUhbjAXiPZard89TfqZ4c58PSX9JSsMcc2

Merkle Root

8e23b0c2315b3f338160b3ca032bd4c760f1e45689a31a31a5e7112c2e56329d

Transactions (3)

Coinbase7657c05cec8a9f…40946bd58959ac

1 in → 1 out11.6700 XPM109 B

AUhbjAXi…9JSsMcc2

bd11b6e0628111…3b20c3b1001516

1 in → 2 out7.5237 XPM227 B

AaCZiFay…6oNYPY5h AYBp12R4…aMGVwUmn

bbb4fdfcdd1353…004e6f320e0927

2 in → 2 out6.7533 XPM376 B

AYszgiHe…ZfT5LoJi AQs6RoGM…GF3WFGUb

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.

1.799 × 10¹⁰⁸(109-digit number)

17991192199458352747…73153379005499641039

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

1.799 × 10¹⁰⁸(109-digit number)

17991192199458352747…73153379005499641039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.799 × 10¹⁰⁸(109-digit number)

17991192199458352747…73153379005499641041

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

3.598 × 10¹⁰⁸(109-digit number)

35982384398916705494…46306758010999282079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.598 × 10¹⁰⁸(109-digit number)

35982384398916705494…46306758010999282081

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

7.196 × 10¹⁰⁸(109-digit number)

71964768797833410989…92613516021998564159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.196 × 10¹⁰⁸(109-digit number)

71964768797833410989…92613516021998564161

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

1.439 × 10¹⁰⁹(110-digit number)

14392953759566682197…85227032043997128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.439 × 10¹⁰⁹(110-digit number)

14392953759566682197…85227032043997128321

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

2.878 × 10¹⁰⁹(110-digit number)

28785907519133364395…70454064087994256639

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 #89,575

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