Block #677,043

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/14/2014, 3:35:10 AM · Difficulty 10.9647 · 6,127,962 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cbc9cfb1afa00a14e43b6124c2b89d9dd0da8235ad0a44226dd0292804693dcb

View on Chainz ↗

Height

#677,043

Difficulty

10.964696

Transactions

Size

990 B

Version

Bits

0af6f64d

Nonce

2,461,190,380

Timestamp

8/14/2014, 3:35:10 AM

Confirmations

6,127,962

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8f5826d2143e84fd9012d0f3e05529022fef1794d44e4f689f00ce6df79586fb

Transactions (3)

Coinbase4ec03733778bed…c23f971422b26e

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

599b760c956c8d…051679ec548733

3 in → 2 out10.1628 XPM523 B

AZFyR8n4…Xiiavx12 ARrMFRvL…MRVKiVRU

5f25e4e6c9e95a…4881613ba70eca

1 in → 3 out6.0644 XPM261 B

AGhhvnpP…QBGxYmtJ AeKNrjNj…1NEq95Ta ALcuyVHq…GqBQvzUr

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.

1.676 × 10⁹⁴(95-digit number)

16761497536392949302…50779500199919466399

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

1.676 × 10⁹⁴(95-digit number)

16761497536392949302…50779500199919466399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.676 × 10⁹⁴(95-digit number)

16761497536392949302…50779500199919466401

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

3.352 × 10⁹⁴(95-digit number)

33522995072785898605…01559000399838932799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.352 × 10⁹⁴(95-digit number)

33522995072785898605…01559000399838932801

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

6.704 × 10⁹⁴(95-digit number)

67045990145571797211…03118000799677865599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.704 × 10⁹⁴(95-digit number)

67045990145571797211…03118000799677865601

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

1.340 × 10⁹⁵(96-digit number)

13409198029114359442…06236001599355731199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.340 × 10⁹⁵(96-digit number)

13409198029114359442…06236001599355731201

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

2.681 × 10⁹⁵(96-digit number)

26818396058228718884…12472003198711462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.681 × 10⁹⁵(96-digit number)

26818396058228718884…12472003198711462401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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