Block #78,443

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 9:57:26 PM · Difficulty 9.2197 · 6,713,109 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22798fae8a82ab80bf56299e56332151021534d7a1f7bade093d149d38f2f249

View on Chainz ↗

Height

#78,443

Difficulty

9.219734

Transactions

Size

132.14 KB

Version

Bits

0938407c

Nonce

131

Timestamp

7/22/2013, 9:57:26 PM

Confirmations

6,713,109

Merkle Root

08c38e997366801bcfe2b4322da99ae0c3c08304b9ded41c012102d879e11ef6

Transactions (3)

Coinbasee7f04ac32eaa72…21e4f60084ba5c

1 in → 1 out13.1200 XPM110 B

ANV4R6A8…hFA3XgLz

4d19a79179e1c8…bd9b5d4c9020f2

581 in → 1 out10000.0000 XPM65.38 KB

AVWgfMdX…zxMSzJm5

e245be126ff2f1…a4bf65299e526f

592 in → 1 out10000.0000 XPM66.57 KB

AVWgfMdX…zxMSzJm5

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.

6.671 × 10⁸⁸(89-digit number)

66715223840131125325…25657750330649927579

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

6.671 × 10⁸⁸(89-digit number)

66715223840131125325…25657750330649927579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.671 × 10⁸⁸(89-digit number)

66715223840131125325…25657750330649927581

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

1.334 × 10⁸⁹(90-digit number)

13343044768026225065…51315500661299855159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.334 × 10⁸⁹(90-digit number)

13343044768026225065…51315500661299855161

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

2.668 × 10⁸⁹(90-digit number)

26686089536052450130…02631001322599710319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.668 × 10⁸⁹(90-digit number)

26686089536052450130…02631001322599710321

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

5.337 × 10⁸⁹(90-digit number)

53372179072104900260…05262002645199420639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.337 × 10⁸⁹(90-digit number)

53372179072104900260…05262002645199420641

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

1.067 × 10⁹⁰(91-digit number)

10674435814420980052…10524005290398841279

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