Block #78,080

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 4:23:48 PM · Difficulty 9.2152 · 6,748,034 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e8339a4825a27bbbfe67657b52d61c59effd7862f550799090044c472b8c830

View on Chainz ↗

Height

#78,080

Difficulty

9.215228

Transactions

Size

437 B

Version

Bits

09371927

Nonce

271

Timestamp

7/22/2013, 4:23:48 PM

Confirmations

6,748,034

Mined by

⛏️ P2SHAbZxux7m9SGMpVhYoq6pKJVA3vFeGrgxjo

Merkle Root

b96224a4aadc637a983c3a48fa62da59f0bee43c90f41ab5ab2da7780c908151

Transactions (2)

Coinbasedcfd629cde1cfc…78fe534feed4d0

1 in → 1 out11.7700 XPM110 B

AbZxux7m…FeGrgxjo

7fb25719403821…a2a838e1fcbd63

1 in → 2 out15.6300 XPM225 B

AKGcn9MF…mqnPWkPr AQS8AL8g…GyKwhe6J

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.

8.847 × 10¹²²(123-digit number)

88477938849852595879…50702067933054253599

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

8.847 × 10¹²²(123-digit number)

88477938849852595879…50702067933054253599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.847 × 10¹²²(123-digit number)

88477938849852595879…50702067933054253601

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

1.769 × 10¹²³(124-digit number)

17695587769970519175…01404135866108507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.769 × 10¹²³(124-digit number)

17695587769970519175…01404135866108507201

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

3.539 × 10¹²³(124-digit number)

35391175539941038351…02808271732217014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.539 × 10¹²³(124-digit number)

35391175539941038351…02808271732217014401

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

7.078 × 10¹²³(124-digit number)

70782351079882076703…05616543464434028799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.078 × 10¹²³(124-digit number)

70782351079882076703…05616543464434028801

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

1.415 × 10¹²⁴(125-digit number)

14156470215976415340…11233086928868057599

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

Block #78,080

Cookie Preferences