Block #86,053

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 9:01:07 PM · Difficulty 9.2891 · 6,713,306 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46d2346b5353c9824d5bd3e5af3db7629f11b074a0bcf274451632035557a13a

View on Chainz ↗

Height

#86,053

Difficulty

9.289085

Transactions

Size

397 B

Version

Bits

094a0177

Nonce

17,736

Timestamp

7/27/2013, 9:01:07 PM

Confirmations

6,713,306

Mined by

⛏️ P2SHASVXe8jAtgDpqZYkYbn6PhBC2G88uC7Ts7

Merkle Root

ed81c9113f0c97861fc90a552d2f4e8c8d084df8793f30ce7fd5dbe47bcfba1a

Transactions (2)

Coinbased0e0b90993b2b9…a6078824c2fa43

1 in → 1 out11.5800 XPM109 B

ASVXe8jA…88uC7Ts7

c6ebacc4b6ceb6…c247cbf5f8221b

1 in → 2 out11.5900 XPM192 B

AcqZuz9i…DGngwSZs AGfz3APU…kNJNtgfb

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.

7.634 × 10¹⁰⁸(109-digit number)

76346932565922402696…57531716812855909759

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

7.634 × 10¹⁰⁸(109-digit number)

76346932565922402696…57531716812855909759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.634 × 10¹⁰⁸(109-digit number)

76346932565922402696…57531716812855909761

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

1.526 × 10¹⁰⁹(110-digit number)

15269386513184480539…15063433625711819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.526 × 10¹⁰⁹(110-digit number)

15269386513184480539…15063433625711819521

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

3.053 × 10¹⁰⁹(110-digit number)

30538773026368961078…30126867251423639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.053 × 10¹⁰⁹(110-digit number)

30538773026368961078…30126867251423639041

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

6.107 × 10¹⁰⁹(110-digit number)

61077546052737922157…60253734502847278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.107 × 10¹⁰⁹(110-digit number)

61077546052737922157…60253734502847278081

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

1.221 × 10¹¹⁰(111-digit number)

12215509210547584431…20507469005694556159

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