Block #428,978

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 11:48:56 AM · Difficulty 10.3429 · 6,382,098 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06f48c5fcfa6ae11551d6a44c5d0baa3a37f210b44f5f8ba61e5bbb3e2db276a

View on Chainz ↗

Height

#428,978

Difficulty

10.342866

Transactions

Size

1.90 KB

Version

Bits

0a57c613

Nonce

126,562

Timestamp

3/4/2014, 11:48:56 AM

Confirmations

6,382,098

Mined by

⛏️ BbAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

445457e2bb769e0334f33ecbaadccce06d4d3e591f6cb739450fd615d5dccb5d

Transactions (2)

Coinbase3e16b303a8bd0a…5db9ef4b31b739

1 in → 22 out9.3540 XPM811 B

AdFLJFhb…bsaVkAyh Adnmwr7c…BticWu6P AUzEPJFG…kYkA5U9V AcuM7XiJ…5uND8Jce AVRMvm7T…6PC6keBx

cbe870ffa0aadb…c51449577dd148

7 in → 1 out10.0000 XPM1.02 KB

ASoXp2As…edjAmBXG

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.

1.129 × 10⁹³(94-digit number)

11298294191594334820…11553675259578407999

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

1.129 × 10⁹³(94-digit number)

11298294191594334820…11553675259578407999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.129 × 10⁹³(94-digit number)

11298294191594334820…11553675259578408001

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

2.259 × 10⁹³(94-digit number)

22596588383188669641…23107350519156815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.259 × 10⁹³(94-digit number)

22596588383188669641…23107350519156816001

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

4.519 × 10⁹³(94-digit number)

45193176766377339283…46214701038313631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.519 × 10⁹³(94-digit number)

45193176766377339283…46214701038313632001

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

9.038 × 10⁹³(94-digit number)

90386353532754678567…92429402076627263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.038 × 10⁹³(94-digit number)

90386353532754678567…92429402076627264001

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

1.807 × 10⁹⁴(95-digit number)

18077270706550935713…84858804153254527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.807 × 10⁹⁴(95-digit number)

18077270706550935713…84858804153254528001

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 #428,978

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