Block #714,992

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/10/2014, 11:55:21 AM · Difficulty 10.9545 · 6,095,263 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7db41a1d14c46624786472b3a3b917f892ceb526a42a856a0df88586e25ca86

View on Chainz ↗

Height

#714,992

Difficulty

10.954466

Transactions

Size

8.96 KB

Version

Bits

0af457dd

Nonce

98,152,705

Timestamp

9/10/2014, 11:55:21 AM

Confirmations

6,095,263

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8c93f5cdbd8cf97be6471fba76e1688402189f6b33d2a567e91fe0c6f32695b9

Transactions (4)

Coinbase5923f9f8d75818…d72a0d9e9d6c45

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

54b7942136f727…046a9a23859b71

57 in → 2 out1000.0100 XPM8.32 KB

AcNmMse1…r8N9XMXx AMxVvtAh…7NPLWKjj

2fa88ab00c8b3d…4a0545105c0c46

1 in → 2 out6.4800 XPM225 B

ATjwywoV…ga9eRXwi AeFLsqLa…KosTzap5

ee3998a923e7d2…866f85c578a6b0

1 in → 2 out5.9322 XPM225 B

AKxVRZZG…C8dW4fF8 Abs1CTRR…uk6ieBYF

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.

1.607 × 10⁹⁸(99-digit number)

16072701840254583507…04478437212658099199

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

1.607 × 10⁹⁸(99-digit number)

16072701840254583507…04478437212658099199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.607 × 10⁹⁸(99-digit number)

16072701840254583507…04478437212658099201

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

3.214 × 10⁹⁸(99-digit number)

32145403680509167015…08956874425316198399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.214 × 10⁹⁸(99-digit number)

32145403680509167015…08956874425316198401

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

6.429 × 10⁹⁸(99-digit number)

64290807361018334031…17913748850632396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.429 × 10⁹⁸(99-digit number)

64290807361018334031…17913748850632396801

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

1.285 × 10⁹⁹(100-digit number)

12858161472203666806…35827497701264793599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.285 × 10⁹⁹(100-digit number)

12858161472203666806…35827497701264793601

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

2.571 × 10⁹⁹(100-digit number)

25716322944407333612…71654995402529587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.571 × 10⁹⁹(100-digit number)

25716322944407333612…71654995402529587201

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

5.143 × 10⁹⁹(100-digit number)

51432645888814667225…43309990805059174399

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 #714,992

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