Block #59,351

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 1:37:05 AM · Difficulty 8.9645 · 6,730,432 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

317ab62ba3259abf2cfa34bf0eb0fefcab2f4157dc4af207f6e432c3affe25ba

View on Chainz ↗

Height

#59,351

Difficulty

8.964548

Transactions

Size

1.31 KB

Version

Bits

08f6eca0

Nonce

681

Timestamp

7/18/2013, 1:37:05 AM

Confirmations

6,730,432

Merkle Root

a2963b3d2a618672b89b1f00c182de37330ad2bc042736b86407f937b337a651

Transactions (2)

Coinbase2e04fc69541744…61ff02190b0cf6

1 in → 1 out12.4500 XPM109 B

ALYmQb7H…ezgZdaes

8458268035ac7e…e1cb2916ac2ece

9 in → 1 out125.0000 XPM1.11 KB

AYxoT5K3…VLfpXK9w

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.

4.445 × 10¹¹³(114-digit number)

44459090781075746291…44485501430094368939

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

4.445 × 10¹¹³(114-digit number)

44459090781075746291…44485501430094368939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.445 × 10¹¹³(114-digit number)

44459090781075746291…44485501430094368941

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

8.891 × 10¹¹³(114-digit number)

88918181562151492582…88971002860188737879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.891 × 10¹¹³(114-digit number)

88918181562151492582…88971002860188737881

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

1.778 × 10¹¹⁴(115-digit number)

17783636312430298516…77942005720377475759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.778 × 10¹¹⁴(115-digit number)

17783636312430298516…77942005720377475761

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

3.556 × 10¹¹⁴(115-digit number)

35567272624860597033…55884011440754951519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.556 × 10¹¹⁴(115-digit number)

35567272624860597033…55884011440754951521

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

7.113 × 10¹¹⁴(115-digit number)

71134545249721194066…11768022881509903039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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