Block #418,961

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 6:53:16 AM · Difficulty 10.3832 · 6,398,882 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d687c0f9f63e3eee7f1503d4fabf54de2d4f4db2b77c1cad1808de05890792bc

View on Chainz ↗

Height

#418,961

Difficulty

10.383216

Transactions

Size

868 B

Version

Bits

0a621a78

Nonce

38,946

Timestamp

2/25/2014, 6:53:16 AM

Confirmations

6,398,882

Mined by

⛏️ daS=AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dda6e0a81a8459eb1c05f23c412c8a7acc09f99b52aade7f8bd281035dd5b8e4

Transactions (1)

Coinbasedda6e0a81a8459…d281035dd5b8e4

1 in → 21 out9.2600 XPM777 B

AQvZBsUo…hppgRZTJ ATYWyzAn…dzCMeJD1 AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6

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.

7.080 × 10⁹⁶(97-digit number)

70800733575977918272…40888536678775507199

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

7.080 × 10⁹⁶(97-digit number)

70800733575977918272…40888536678775507199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.080 × 10⁹⁶(97-digit number)

70800733575977918272…40888536678775507201

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

1.416 × 10⁹⁷(98-digit number)

14160146715195583654…81777073357551014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.416 × 10⁹⁷(98-digit number)

14160146715195583654…81777073357551014401

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

2.832 × 10⁹⁷(98-digit number)

28320293430391167308…63554146715102028799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.832 × 10⁹⁷(98-digit number)

28320293430391167308…63554146715102028801

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

5.664 × 10⁹⁷(98-digit number)

56640586860782334617…27108293430204057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.664 × 10⁹⁷(98-digit number)

56640586860782334617…27108293430204057601

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

1.132 × 10⁹⁸(99-digit number)

11328117372156466923…54216586860408115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.132 × 10⁹⁸(99-digit number)

11328117372156466923…54216586860408115201

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 #418,961

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