Block #756,913

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/8/2014, 3:08:22 PM · Difficulty 10.9671 · 6,086,863 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de7d011156a02d65c4c05115c8eaea0acb5bcb730cc4dae00567c23bbb68785a

View on Chainz ↗

Height

#756,913

Difficulty

10.967081

Transactions

Size

6.35 KB

Version

Bits

0af792a2

Nonce

521,044,764

Timestamp

10/8/2014, 3:08:22 PM

Confirmations

6,086,863

Mined by

⛏️ P2SHAWg1s88ehoA6zQiG5pamghYcQduAJsem1A

Merkle Root

1c350d6d28cf069ca05ba7f2c4600f024b66301e472bc1c800c29770ac78aa89

Transactions (4)

Coinbase4cfb1236a0d5ea…433fcd81ea475d

1 in → 1 out8.3800 XPM110 B

AWg1s88e…uAJsem1A

413c5ad1cf5a8c…c802f6952234c4

39 in → 2 out200.0105 XPM5.72 KB

ATQmKHmq…mhYoD6Lz ALRuXegM…qhkfJpvU

956f6adde148d3…bf0099c26d1239

1 in → 2 out2.4964 XPM225 B

AVeoKEHW…hGQjMhDV AQf4oh3T…qfRSQ4Aq

e81a6913f59ad4…4369f5d0441906

1 in → 2 out1.2351 XPM226 B

AY7FXqSf…ZyQmDYgZ ASx9RPHT…8fVzc2Ey

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.

3.366 × 10⁹¹(92-digit number)

33667601381850463029…86217746014543943039

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

3.366 × 10⁹¹(92-digit number)

33667601381850463029…86217746014543943039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.366 × 10⁹¹(92-digit number)

33667601381850463029…86217746014543943041

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

6.733 × 10⁹¹(92-digit number)

67335202763700926058…72435492029087886079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.733 × 10⁹¹(92-digit number)

67335202763700926058…72435492029087886081

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

1.346 × 10⁹²(93-digit number)

13467040552740185211…44870984058175772159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.346 × 10⁹²(93-digit number)

13467040552740185211…44870984058175772161

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

2.693 × 10⁹²(93-digit number)

26934081105480370423…89741968116351544319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.693 × 10⁹²(93-digit number)

26934081105480370423…89741968116351544321

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

5.386 × 10⁹²(93-digit number)

53868162210960740846…79483936232703088639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.386 × 10⁹²(93-digit number)

53868162210960740846…79483936232703088641

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

1.077 × 10⁹³(94-digit number)

10773632442192148169…58967872465406177279

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 #756,913

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