Block #647,620

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/25/2014, 6:05:54 PM · Difficulty 10.9514 · 6,177,187 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1af7cf09b698eccf3f3b92479e2e0243b5ac5299b21381352a2d8dff14bd8d8a

View on Chainz ↗

Height

#647,620

Difficulty

10.951435

Transactions

Size

501 B

Version

Bits

0af3913f

Nonce

352,753,640

Timestamp

7/25/2014, 6:05:54 PM

Confirmations

6,177,187

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

14264968d94695e754c1447d3cbaacf14fac496c73113ffbd5e7f303f3874707

Transactions (2)

Coinbase27b2845d77b7eb…bf282db28b99bf

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

d2944a405781df…841f8f1e5aa1c8

1 in → 5 out8.3100 XPM293 B

AeKNrjNj…1NEq95Ta ALxaSzoH…c8tfqwKi AZdy7tMB…bWoKDJVg AZa2QvH4…JvH9i3cj Aeff3baB…A5fkk3mo

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.

3.959 × 10¹⁰⁰(101-digit number)

39594958501781710353…45067479430254673919

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

3.959 × 10¹⁰⁰(101-digit number)

39594958501781710353…45067479430254673919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.959 × 10¹⁰⁰(101-digit number)

39594958501781710353…45067479430254673921

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

7.918 × 10¹⁰⁰(101-digit number)

79189917003563420706…90134958860509347839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.918 × 10¹⁰⁰(101-digit number)

79189917003563420706…90134958860509347841

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

1.583 × 10¹⁰¹(102-digit number)

15837983400712684141…80269917721018695679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.583 × 10¹⁰¹(102-digit number)

15837983400712684141…80269917721018695681

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

3.167 × 10¹⁰¹(102-digit number)

31675966801425368282…60539835442037391359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.167 × 10¹⁰¹(102-digit number)

31675966801425368282…60539835442037391361

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

6.335 × 10¹⁰¹(102-digit number)

63351933602850736564…21079670884074782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.335 × 10¹⁰¹(102-digit number)

63351933602850736564…21079670884074782721

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

Block #647,620

Cookie Preferences