Block #86,506

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 4:40:55 AM · Difficulty 9.2883 · 6,719,765 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2430375555ad3c56d4f6b60d830e46f01bc9021497ebd591466a0cee1ee1f5ae

View on Chainz ↗

Height

#86,506

Difficulty

9.288332

Transactions

Size

1.01 KB

Version

Bits

0949d01e

Nonce

59,126

Timestamp

7/28/2013, 4:40:55 AM

Confirmations

6,719,765

Mined by

⛏️ P2SHAW488pqTSYSYTvSTu73mDhuFYF1g8H1mFa

Merkle Root

9548c5dcd997709c448b76d5d4095e474d7a9bb66d6b4d2488605d6265853b61

Transactions (3)

Coinbase1102c2a66d2408…f8007dcaead612

1 in → 1 out11.5900 XPM109 B

AW488pqT…1g8H1mFa

9503a4f87917a1…9b6df9b3d26ff8

3 in → 2 out24.4700 XPM455 B

AR8rZC7v…Y6NaRp77 ARFXJrdj…LUdkymq1

fa71ad40c22b7b…9c6c966baa7db5

2 in → 2 out0.1056 XPM374 B

AeHoKLZb…Wy1577ib AN3WY121…RULmrS71

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.

1.044 × 10¹¹⁷(118-digit number)

10445445682902232062…17729784820995187199

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

1.044 × 10¹¹⁷(118-digit number)

10445445682902232062…17729784820995187199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.044 × 10¹¹⁷(118-digit number)

10445445682902232062…17729784820995187201

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

2.089 × 10¹¹⁷(118-digit number)

20890891365804464124…35459569641990374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.089 × 10¹¹⁷(118-digit number)

20890891365804464124…35459569641990374401

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

4.178 × 10¹¹⁷(118-digit number)

41781782731608928249…70919139283980748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.178 × 10¹¹⁷(118-digit number)

41781782731608928249…70919139283980748801

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

8.356 × 10¹¹⁷(118-digit number)

83563565463217856498…41838278567961497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.356 × 10¹¹⁷(118-digit number)

83563565463217856498…41838278567961497601

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

1.671 × 10¹¹⁸(119-digit number)

16712713092643571299…83676557135922995199

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 #86,506

Cookie Preferences