Block #421,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 6:26:21 AM · Difficulty 10.3741 · 6,404,844 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c12da786f7fa53eae539e06a588c0aaccaae7578d100c4c650019d06d1987aba

View on Chainz ↗

Height

#421,729

Difficulty

10.374059

Transactions

Size

772 B

Version

Bits

0a5fc24f

Nonce

51,740

Timestamp

2/27/2014, 6:26:21 AM

Confirmations

6,404,844

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ef8973acbff639617c803db69a0262457ff625b372aa5de5529015aefc208b54

Transactions (3)

Coinbasece3395affedbb0…f4323708875f95

1 in → 1 out9.3000 XPM116 B

AbwWkWZt…kawDhufa

3416e46bbed8d1…1eff79325f55f6

2 in → 2 out198.5853 XPM373 B

AQAZyBD7…5BYEWEzT AJBppmqW…4MtG7fV9

460fdb34504451…9974a86be2685e

1 in → 2 out9.2400 XPM191 B

AJbq7Mk7…NKwRjJLP AFtxgt2M…rktPKGHw

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.

3.689 × 10⁹⁸(99-digit number)

36891360546502523161…00033286040045704319

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

3.689 × 10⁹⁸(99-digit number)

36891360546502523161…00033286040045704319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.689 × 10⁹⁸(99-digit number)

36891360546502523161…00033286040045704321

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

7.378 × 10⁹⁸(99-digit number)

73782721093005046322…00066572080091408639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.378 × 10⁹⁸(99-digit number)

73782721093005046322…00066572080091408641

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

1.475 × 10⁹⁹(100-digit number)

14756544218601009264…00133144160182817279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.475 × 10⁹⁹(100-digit number)

14756544218601009264…00133144160182817281

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

2.951 × 10⁹⁹(100-digit number)

29513088437202018528…00266288320365634559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.951 × 10⁹⁹(100-digit number)

29513088437202018528…00266288320365634561

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

5.902 × 10⁹⁹(100-digit number)

59026176874404037057…00532576640731269119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.902 × 10⁹⁹(100-digit number)

59026176874404037057…00532576640731269121

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 #421,729

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