Block #639,443

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/19/2014, 9:41:23 AM · Difficulty 10.9597 · 6,177,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76e626563e28fbbd79e75ced59c4e0feac186fb19d9b758302e4e6d576f0ea11

View on Chainz ↗

Height

#639,443

Difficulty

10.959701

Transactions

Size

807 B

Version

Bits

0af5aeef

Nonce

476,908,153

Timestamp

7/19/2014, 9:41:23 AM

Confirmations

6,177,316

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c319569329947f0bd55a16f6977988433248af6255c0eb4920610c8381072eef

Transactions (3)

Coinbase7086c916cdc5bf…ad13bd7c3ba77a

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

e2c872f70a77ad…57f0c6cb4f3aeb

2 in → 2 out16.6200 XPM375 B

AJzjuYh3…ndhqFVng AYmYWKQT…1GRFkwJV

fad46ca6e611be…0211061074ac6d

1 in → 2 out8.3000 XPM226 B

ATxoEAVm…o1hPnNf4 ATScQPoL…zG9R2APw

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.

1.006 × 10⁹⁴(95-digit number)

10061297689865159747…29854823813411321519

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

1.006 × 10⁹⁴(95-digit number)

10061297689865159747…29854823813411321519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.006 × 10⁹⁴(95-digit number)

10061297689865159747…29854823813411321521

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

2.012 × 10⁹⁴(95-digit number)

20122595379730319495…59709647626822643039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.012 × 10⁹⁴(95-digit number)

20122595379730319495…59709647626822643041

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

4.024 × 10⁹⁴(95-digit number)

40245190759460638990…19419295253645286079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.024 × 10⁹⁴(95-digit number)

40245190759460638990…19419295253645286081

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

8.049 × 10⁹⁴(95-digit number)

80490381518921277980…38838590507290572159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.049 × 10⁹⁴(95-digit number)

80490381518921277980…38838590507290572161

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

1.609 × 10⁹⁵(96-digit number)

16098076303784255596…77677181014581144319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.609 × 10⁹⁵(96-digit number)

16098076303784255596…77677181014581144321

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

3.219 × 10⁹⁵(96-digit number)

32196152607568511192…55354362029162288639

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 #639,443

Cookie Preferences