Block #71,094

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 5:01:40 PM · Difficulty 8.9928 · 6,722,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4fd002ed7f8c1ab7adb57bc9f8b930c4e7e47f158cad8f30c70788c9d33638f0

View on Chainz ↗

Height

#71,094

Difficulty

8.992841

Transactions

Size

2.96 KB

Version

Bits

08fe2ad2

Nonce

460

Timestamp

7/20/2013, 5:01:40 PM

Confirmations

6,722,448

Merkle Root

cdee0854745d79082a878146fbae010ec98201d2226d27042308c7b9bda92245

Transactions (3)

Coinbaseea2e2e4a0413c1…ca786cb76e47c5

1 in → 1 out12.3900 XPM110 B

AY1D3MPA…DXNxKc8t

7f769c86e05163…bbd6fa184b9921

23 in → 1 out284.2700 XPM2.61 KB

Ab4rdENu…TQCgYmjg

274977da9d461f…297fe76e3fa9f0

1 in → 1 out12.3500 XPM159 B

AaNMrVuB…vz8xMmHF

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.

9.392 × 10¹⁰⁸(109-digit number)

93922652582320953089…46921016341331733339

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

9.392 × 10¹⁰⁸(109-digit number)

93922652582320953089…46921016341331733339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.392 × 10¹⁰⁸(109-digit number)

93922652582320953089…46921016341331733341

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

1.878 × 10¹⁰⁹(110-digit number)

18784530516464190617…93842032682663466679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.878 × 10¹⁰⁹(110-digit number)

18784530516464190617…93842032682663466681

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

3.756 × 10¹⁰⁹(110-digit number)

37569061032928381235…87684065365326933359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.756 × 10¹⁰⁹(110-digit number)

37569061032928381235…87684065365326933361

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

7.513 × 10¹⁰⁹(110-digit number)

75138122065856762471…75368130730653866719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.513 × 10¹⁰⁹(110-digit number)

75138122065856762471…75368130730653866721

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

1.502 × 10¹¹⁰(111-digit number)

15027624413171352494…50736261461307733439

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