Block #505,677

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 2:31:22 PM · Difficulty 10.8116 · 6,309,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ca7e11a8cf05673289f506ee61385135e97275c2d4af79245e8c048e886bd24e

View on Chainz ↗

Height

#505,677

Difficulty

10.811643

Transactions

Size

798 B

Version

Bits

0acfc7d6

Nonce

5,847

Timestamp

4/22/2014, 2:31:22 PM

Confirmations

6,309,176

Mined by

⛏️ MaSV}5AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

13cc86e7ad774d64a6383f5929db6830ca586ef15e75535ff2a6e18ca32ccb6d

Transactions (1)

Coinbase13cc86e7ad774d…a6e18ca32ccb6d

1 in → 19 out8.5400 XPM708 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

1.073 × 10⁹⁴(95-digit number)

10733313919823419010…06485371544736359039

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

1.073 × 10⁹⁴(95-digit number)

10733313919823419010…06485371544736359039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.073 × 10⁹⁴(95-digit number)

10733313919823419010…06485371544736359041

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

2.146 × 10⁹⁴(95-digit number)

21466627839646838021…12970743089472718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.146 × 10⁹⁴(95-digit number)

21466627839646838021…12970743089472718081

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

4.293 × 10⁹⁴(95-digit number)

42933255679293676043…25941486178945436159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.293 × 10⁹⁴(95-digit number)

42933255679293676043…25941486178945436161

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

8.586 × 10⁹⁴(95-digit number)

85866511358587352087…51882972357890872319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.586 × 10⁹⁴(95-digit number)

85866511358587352087…51882972357890872321

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

1.717 × 10⁹⁵(96-digit number)

17173302271717470417…03765944715781744639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.717 × 10⁹⁵(96-digit number)

17173302271717470417…03765944715781744641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #505,677

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