Block #629,437

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/12/2014, 8:05:03 AM · Difficulty 10.9607 · 6,166,226 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e6ec3bd74ec9818630c8c2ac2d43b965534e30ba066b26a195c1e63599f328a

View on Chainz ↗

Height

#629,437

Difficulty

10.960676

Transactions

Size

2.65 KB

Version

Bits

0af5eee1

Nonce

525,291,268

Timestamp

7/12/2014, 8:05:03 AM

Confirmations

6,166,226

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

48375935d73dcbfa0bc8fe30781f3b695c1e8b37ed2f32e20c17e66531fe26d0

Transactions (2)

Coinbase121e78225ed26e…431bbd7c279139

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

ca6a3da039c834…dc67c87c80aafe

10 in → 39 out79.0478 XPM2.45 KB

AGSi2r64…sHAr5uaS AKYyh8o4…cuQQmwbv ARnVzrK6…XYqTgukJ ALVXj14N…RcUDza2k AQHCRLio…2f4qh3rh

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.

5.383 × 10⁹⁵(96-digit number)

53838630644903964649…73910973328917044119

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

5.383 × 10⁹⁵(96-digit number)

53838630644903964649…73910973328917044119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.383 × 10⁹⁵(96-digit number)

53838630644903964649…73910973328917044121

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

1.076 × 10⁹⁶(97-digit number)

10767726128980792929…47821946657834088239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.076 × 10⁹⁶(97-digit number)

10767726128980792929…47821946657834088241

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

2.153 × 10⁹⁶(97-digit number)

21535452257961585859…95643893315668176479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.153 × 10⁹⁶(97-digit number)

21535452257961585859…95643893315668176481

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

4.307 × 10⁹⁶(97-digit number)

43070904515923171719…91287786631336352959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.307 × 10⁹⁶(97-digit number)

43070904515923171719…91287786631336352961

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

8.614 × 10⁹⁶(97-digit number)

86141809031846343439…82575573262672705919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.614 × 10⁹⁶(97-digit number)

86141809031846343439…82575573262672705921

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