Block #427,079

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/3/2014, 3:38:12 AM · Difficulty 10.3454 · 6,381,059 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b2b02cb597920fe63621fabfc8d788127e06b51b00f6ce60dbadb9e5eacf35c

View on Chainz ↗

Height

#427,079

Difficulty

10.345401

Transactions

Size

427 B

Version

Bits

0a586c37

Nonce

402,700

Timestamp

3/3/2014, 3:38:12 AM

Confirmations

6,381,059

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d966fdc13905781c6fe03c3d3f71235f834676fc424d522673a0a7bbeeb4f96f

Transactions (2)

Coinbaseaf58d2cee2e566…aa1bd1eeced194

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

de4edeb1ec205e…ab3a6c9e91de49

1 in → 2 out110588.1903 XPM226 B

AFnh4gYE…H3EF7s2p AZ5ursRH…fUqTHaAb

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.

2.374 × 10⁹⁸(99-digit number)

23746524423447921689…25439124530022748799

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

2.374 × 10⁹⁸(99-digit number)

23746524423447921689…25439124530022748799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.374 × 10⁹⁸(99-digit number)

23746524423447921689…25439124530022748801

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

4.749 × 10⁹⁸(99-digit number)

47493048846895843379…50878249060045497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.749 × 10⁹⁸(99-digit number)

47493048846895843379…50878249060045497601

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

9.498 × 10⁹⁸(99-digit number)

94986097693791686759…01756498120090995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.498 × 10⁹⁸(99-digit number)

94986097693791686759…01756498120090995201

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

1.899 × 10⁹⁹(100-digit number)

18997219538758337351…03512996240181990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.899 × 10⁹⁹(100-digit number)

18997219538758337351…03512996240181990401

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

3.799 × 10⁹⁹(100-digit number)

37994439077516674703…07025992480363980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.799 × 10⁹⁹(100-digit number)

37994439077516674703…07025992480363980801

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.598 × 10⁹⁹(100-digit number)

75988878155033349407…14051984960727961599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #427,079

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