Block #424,019

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 8:57:55 PM · Difficulty 10.3719 · 6,385,640 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2095c1f457341a8e951ed3d62a964057770e81a7f4ff84b62de984815b718f26

View on Chainz ↗

Height

#424,019

Difficulty

10.371850

Transactions

Size

678 B

Version

Bits

0a5f3198

Nonce

42,310

Timestamp

2/28/2014, 8:57:55 PM

Confirmations

6,385,640

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2f407b88677560faef0728d76ea5386fe2d8df90124846f72455c6d827302eae

Transactions (2)

Coinbase5618b200c9454a…52b02ad61b7464

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

3e3c2d48f3295c…660732ca502d29

2 in → 7 out18.5400 XPM477 B

Ad1oK5BF…sRvSLRDv APiJPPBV…oMd88xJd AL6hfYqf…jYfKt9LA AMurAYrb…3iomaSF2 AeKNrjNj…1NEq95Ta

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.

1.416 × 10⁹⁷(98-digit number)

14165453240073494776…24419571888051023919

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

1.416 × 10⁹⁷(98-digit number)

14165453240073494776…24419571888051023919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.416 × 10⁹⁷(98-digit number)

14165453240073494776…24419571888051023921

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

2.833 × 10⁹⁷(98-digit number)

28330906480146989552…48839143776102047839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.833 × 10⁹⁷(98-digit number)

28330906480146989552…48839143776102047841

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

5.666 × 10⁹⁷(98-digit number)

56661812960293979105…97678287552204095679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.666 × 10⁹⁷(98-digit number)

56661812960293979105…97678287552204095681

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

1.133 × 10⁹⁸(99-digit number)

11332362592058795821…95356575104408191359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.133 × 10⁹⁸(99-digit number)

11332362592058795821…95356575104408191361

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

2.266 × 10⁹⁸(99-digit number)

22664725184117591642…90713150208816382719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.266 × 10⁹⁸(99-digit number)

22664725184117591642…90713150208816382721

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 #424,019

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