Block #424,090

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 10:28:14 PM · Difficulty 10.3697 · 6,374,478 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

460bb2a4f611f2a1d1f930e5105408e319d33182403e15c0913d98bb73ce8522

View on Chainz ↗

Height

#424,090

Difficulty

10.369714

Transactions

Size

1.39 KB

Version

Bits

0a5ea594

Nonce

190,383

Timestamp

2/28/2014, 10:28:14 PM

Confirmations

6,374,478

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

529f8ac6d0208a86765d48082f1d997acc8581ca895d456b4b0151b1076e7297

Transactions (3)

Coinbase6e056525fb576b…3c2cc4d68d5c6f

1 in → 1 out9.3200 XPM110 B

AeKNrjNj…1NEq95Ta

35b13e4bce1d45…445023a89dbb2d

1 in → 1 out9.2700 XPM159 B

AXoGMQuL…4AYF9Seh

dc2b403abfb21d…fb5e2c6b7647ad

5 in → 14 out46.3800 XPM1.03 KB

AWJhomny…QAohRN9k AREaYyFH…BMLN62DF AHy24nCY…4KpVC1Hz AHprswVT…7ysvGhPF AQGT4dxp…srcbsPWp

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.

7.745 × 10⁹⁷(98-digit number)

77455275506921068762…39604094341270006719

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

7.745 × 10⁹⁷(98-digit number)

77455275506921068762…39604094341270006719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.745 × 10⁹⁷(98-digit number)

77455275506921068762…39604094341270006721

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

1.549 × 10⁹⁸(99-digit number)

15491055101384213752…79208188682540013439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.549 × 10⁹⁸(99-digit number)

15491055101384213752…79208188682540013441

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

3.098 × 10⁹⁸(99-digit number)

30982110202768427505…58416377365080026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.098 × 10⁹⁸(99-digit number)

30982110202768427505…58416377365080026881

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

6.196 × 10⁹⁸(99-digit number)

61964220405536855010…16832754730160053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.196 × 10⁹⁸(99-digit number)

61964220405536855010…16832754730160053761

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

1.239 × 10⁹⁹(100-digit number)

12392844081107371002…33665509460320107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.239 × 10⁹⁹(100-digit number)

12392844081107371002…33665509460320107521

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