Block #714,113

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/9/2014, 7:15:04 PM · Difficulty 10.9555 · 6,080,153 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d4a55378c7557cf6a33620c117e9965b08a6a82ba3546e933dd4e496055e9d1c

View on Chainz ↗

Height

#714,113

Difficulty

10.955504

Transactions

Size

39.94 KB

Version

Bits

0af49be4

Nonce

889,112,521

Timestamp

9/9/2014, 7:15:04 PM

Confirmations

6,080,153

Merkle Root

3669261dc8b43f1ce0b73c0a9aeeecc8f169bf47245e127736bdbfb3f7bee3dd

Transactions (3)

Coinbase5c0fe2dad0e336…831098d47e4b0a

1 in → 1 out8.7400 XPM116 B

ANSXnLY2…Sd25TjkD

51abe8e60c0f8a…39dcdb2f64a866

261 in → 2 out491.8572 XPM37.78 KB

AbGd9SE5…rnLHZv6P AX5bEVN5…zrs8FPJF

3108eb0b42627a…c85329296eeb11

13 in → 2 out87.0130 XPM1.96 KB

AWkdeMFz…8VqzqvKd AcCRATsw…3zgq51a9

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.

7.904 × 10⁹⁴(95-digit number)

79041400743055984357…25440239870130187459

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

7.904 × 10⁹⁴(95-digit number)

79041400743055984357…25440239870130187459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.904 × 10⁹⁴(95-digit number)

79041400743055984357…25440239870130187461

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

1.580 × 10⁹⁵(96-digit number)

15808280148611196871…50880479740260374919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.580 × 10⁹⁵(96-digit number)

15808280148611196871…50880479740260374921

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

3.161 × 10⁹⁵(96-digit number)

31616560297222393743…01760959480520749839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.161 × 10⁹⁵(96-digit number)

31616560297222393743…01760959480520749841

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

6.323 × 10⁹⁵(96-digit number)

63233120594444787486…03521918961041499679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.323 × 10⁹⁵(96-digit number)

63233120594444787486…03521918961041499681

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

1.264 × 10⁹⁶(97-digit number)

12646624118888957497…07043837922082999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.264 × 10⁹⁶(97-digit number)

12646624118888957497…07043837922082999361

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

2.529 × 10⁹⁶(97-digit number)

25293248237777914994…14087675844165998719

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