Block #85,099

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 5:46:40 AM · Difficulty 9.2836 · 6,706,888 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e106cf8bca572901c84328b2a66072f7e6b2344b016e64211eca575bc4b91d5

View on Chainz ↗

Height

#85,099

Difficulty

9.283551

Transactions

Size

1.61 KB

Version

Bits

094896c9

Nonce

141,441

Timestamp

7/27/2013, 5:46:40 AM

Confirmations

6,706,888

Merkle Root

2ed919b48113665780c673171b101521bcb3ac1cc05699338ba8dec137711f57

Transactions (2)

Coinbasef8be4150fe7a69…bfa12a57560e8e

1 in → 1 out11.6100 XPM109 B

APHTti5k…Tw8ZiGPs

bbb2a74c70a93b…d8d3af4c5c109e

12 in → 2 out139.4500 XPM1.41 KB

AJc7ETo3…y5s7mhvH AUckWJ4d…rccphzch

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.

4.736 × 10¹⁰⁸(109-digit number)

47369169062665442155…98364120899759832659

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

4.736 × 10¹⁰⁸(109-digit number)

47369169062665442155…98364120899759832659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.736 × 10¹⁰⁸(109-digit number)

47369169062665442155…98364120899759832661

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

9.473 × 10¹⁰⁸(109-digit number)

94738338125330884311…96728241799519665319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.473 × 10¹⁰⁸(109-digit number)

94738338125330884311…96728241799519665321

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

1.894 × 10¹⁰⁹(110-digit number)

18947667625066176862…93456483599039330639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.894 × 10¹⁰⁹(110-digit number)

18947667625066176862…93456483599039330641

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

3.789 × 10¹⁰⁹(110-digit number)

37895335250132353724…86912967198078661279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.789 × 10¹⁰⁹(110-digit number)

37895335250132353724…86912967198078661281

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

7.579 × 10¹⁰⁹(110-digit number)

75790670500264707449…73825934396157322559

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