Block #58,398

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 8:24:45 PM · Difficulty 8.9597 · 6,758,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f11d1f08ae1427ecf4640ecd723ea631114abf36b975f0272b6b62d91b94462e

View on Chainz ↗

Height

#58,398

Difficulty

8.959677

Transactions

Size

1.15 KB

Version

Bits

08f5ad65

Nonce

153

Timestamp

7/17/2013, 8:24:45 PM

Confirmations

6,758,198

Mined by

⛏️ P2SHAMRJBb3V94CDPb3SssTj1B2eiHZv15uY6D

Merkle Root

a44d38b40b465a280188f5694160727d9eb62269c57fb15ca44bd18cff14aa8c

Transactions (3)

Coinbasea7032dc6e1695c…957c5a856a7251

1 in → 1 out12.4600 XPM110 B

AMRJBb3V…Zv15uY6D

b4d709fe437944…7d3a44fa6b36da

5 in → 2 out1508.1667 XPM820 B

AZSbYoGn…qNua3NtH AURQgrhK…xf25SUj9

f9d0e0615fe7c3…a06e8f7ba3710c

1 in → 1 out14.2000 XPM157 B

AUwoythQ…6kg4mtGm

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.

2.830 × 10⁹⁰(91-digit number)

28309644449749615159…41406031742697390359

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

2.830 × 10⁹⁰(91-digit number)

28309644449749615159…41406031742697390359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.830 × 10⁹⁰(91-digit number)

28309644449749615159…41406031742697390361

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

5.661 × 10⁹⁰(91-digit number)

56619288899499230318…82812063485394780719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.661 × 10⁹⁰(91-digit number)

56619288899499230318…82812063485394780721

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

1.132 × 10⁹¹(92-digit number)

11323857779899846063…65624126970789561439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.132 × 10⁹¹(92-digit number)

11323857779899846063…65624126970789561441

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

2.264 × 10⁹¹(92-digit number)

22647715559799692127…31248253941579122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.264 × 10⁹¹(92-digit number)

22647715559799692127…31248253941579122881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #58,398

Cookie Preferences