Block #421,279

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 10:25:32 PM · Difficulty 10.3775 · 6,373,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2f90e127d4fa5988166121b0b83f8f18d614d51004ccaa21d7bf4de907246e6

View on Chainz ↗

Height

#421,279

Difficulty

10.377498

Transactions

Size

1.80 KB

Version

Bits

0a60a3bb

Nonce

185,299

Timestamp

2/26/2014, 10:25:32 PM

Confirmations

6,373,575

Mined by

⛏️ P2SHATbfdtueDfAbEXc3c81jY9D3vQYwyPrhjz

Merkle Root

b53f6a8e149f21e7244ccbe8395aa08f9c340d9db4492ac69227640ab6141d2e

Transactions (2)

Coinbasedda21044cedd52…abe0533679bdae

1 in → 1 out9.2900 XPM109 B

ATbfdtue…YwyPrhjz

bacf521020c087…d654241658b9f8

8 in → 21 out74.0716 XPM1.60 KB

AcMeLfum…YY1QUUC8 AWLJDESt…yksNKdoy ASo6tkxs…RE3HVviz ASo6ts9T…gkEQsdPi AdkZ3hkz…JCYhZRGU

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.

1.429 × 10⁹⁸(99-digit number)

14293898320635992882…89703621662938817759

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

1.429 × 10⁹⁸(99-digit number)

14293898320635992882…89703621662938817759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.429 × 10⁹⁸(99-digit number)

14293898320635992882…89703621662938817761

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

2.858 × 10⁹⁸(99-digit number)

28587796641271985764…79407243325877635519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.858 × 10⁹⁸(99-digit number)

28587796641271985764…79407243325877635521

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

5.717 × 10⁹⁸(99-digit number)

57175593282543971528…58814486651755271039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.717 × 10⁹⁸(99-digit number)

57175593282543971528…58814486651755271041

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

1.143 × 10⁹⁹(100-digit number)

11435118656508794305…17628973303510542079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.143 × 10⁹⁹(100-digit number)

11435118656508794305…17628973303510542081

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

2.287 × 10⁹⁹(100-digit number)

22870237313017588611…35257946607021084159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.287 × 10⁹⁹(100-digit number)

22870237313017588611…35257946607021084161

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