Block #745,697

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/29/2014, 4:36:20 AM · Difficulty 10.9792 · 6,081,603 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad4549928940ec8a5a04484bd13a37643cb8f8960fdd88902eead4e8ca61e17f

View on Chainz ↗

Height

#745,697

Difficulty

10.979164

Transactions

Size

1.09 KB

Version

Bits

0afaaa80

Nonce

697,741,262

Timestamp

9/29/2014, 4:36:20 AM

Confirmations

6,081,603

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dd383d7984a0edb9d5c2018d35de7a6bc348617e874b3165da5dd7a2beb19e8f

Transactions (5)

Coinbase4c1cff8c2168d1…01c7c03b4f1097

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

f70a67ab059538…f795e7046b93ed

1 in → 2 out8.2700 XPM225 B

AQUoQzW3…ZKDNaG2E AdhVTych…g8Rp4HWM

a397fa99b508fd…fce82db4a5a416

1 in → 2 out8.2700 XPM227 B

AJNQZFmQ…oY2RP3Pa AG6CnYJW…1cC6rUFD

f8649ebfb0e92d…ad5b64f652060a

1 in → 2 out8.2700 XPM227 B

AP4Nt2LZ…X4WHSMxB AaF1rWqu…rpTE5LwQ

ad83c46eab0cb8…9f6ed4148a3b1c

1 in → 2 out8.2700 XPM226 B

AHxEi2gi…kjr8JVNi AbEHpita…RpeBpsSe

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.

2.342 × 10⁹⁹(100-digit number)

23421073148240579063…75598474734369505279

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

2.342 × 10⁹⁹(100-digit number)

23421073148240579063…75598474734369505279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.342 × 10⁹⁹(100-digit number)

23421073148240579063…75598474734369505281

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

4.684 × 10⁹⁹(100-digit number)

46842146296481158127…51196949468739010559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.684 × 10⁹⁹(100-digit number)

46842146296481158127…51196949468739010561

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

9.368 × 10⁹⁹(100-digit number)

93684292592962316254…02393898937478021119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.368 × 10⁹⁹(100-digit number)

93684292592962316254…02393898937478021121

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

1.873 × 10¹⁰⁰(101-digit number)

18736858518592463250…04787797874956042239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.873 × 10¹⁰⁰(101-digit number)

18736858518592463250…04787797874956042241

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

3.747 × 10¹⁰⁰(101-digit number)

37473717037184926501…09575595749912084479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.747 × 10¹⁰⁰(101-digit number)

37473717037184926501…09575595749912084481

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

7.494 × 10¹⁰⁰(101-digit number)

74947434074369853003…19151191499824168959

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 #745,697

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