Block #675,752

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/13/2014, 4:44:06 AM · Difficulty 10.9652 · 6,150,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dacd474368d13e92b93a1ea1a79115e7c8682e3c98662504760610ef5061b32f

View on Chainz ↗

Height

#675,752

Difficulty

10.965221

Transactions

Size

433 B

Version

Bits

0af718b2

Nonce

1,901,462,239

Timestamp

8/13/2014, 4:44:06 AM

Confirmations

6,150,760

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0e5dc8c79d07cb6697d0c6d5885fea54061914cc74e4a99f04402a8040c201d2

Transactions (2)

Coinbase2c77dbaf108684…0b80b7e1012e61

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

565dcf869872fe…e13ffc3b54a9d3

1 in → 2 out19.9940 XPM227 B

Aav4tWgb…aCYEC5Me AJEUQDKb…qwTDUnyQ

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.

5.017 × 10⁹⁴(95-digit number)

50171085357740079247…99171925592873664399

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

5.017 × 10⁹⁴(95-digit number)

50171085357740079247…99171925592873664399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.017 × 10⁹⁴(95-digit number)

50171085357740079247…99171925592873664401

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

1.003 × 10⁹⁵(96-digit number)

10034217071548015849…98343851185747328799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.003 × 10⁹⁵(96-digit number)

10034217071548015849…98343851185747328801

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

2.006 × 10⁹⁵(96-digit number)

20068434143096031698…96687702371494657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.006 × 10⁹⁵(96-digit number)

20068434143096031698…96687702371494657601

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

4.013 × 10⁹⁵(96-digit number)

40136868286192063397…93375404742989315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.013 × 10⁹⁵(96-digit number)

40136868286192063397…93375404742989315201

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

8.027 × 10⁹⁵(96-digit number)

80273736572384126795…86750809485978630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.027 × 10⁹⁵(96-digit number)

80273736572384126795…86750809485978630401

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

1.605 × 10⁹⁶(97-digit number)

16054747314476825359…73501618971957260799

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 #675,752

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