Block #355,602

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 6:23:54 AM · Difficulty 10.3620 · 6,460,328 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f83ada5c28ee201f9745ca6b6f0698c3404403d4a2bd1128810942a384d4df7

View on Chainz ↗

Height

#355,602

Difficulty

10.361952

Transactions

Size

1.53 KB

Version

Bits

0a5ca8e6

Nonce

10,066

Timestamp

1/12/2014, 6:23:54 AM

Confirmations

6,460,328

Mined by

⛏️ mAZwyMUeEeU9toUcpBMpkmWZRnerxMQeLU7

Merkle Root

8abf365418065b8b30f0c11432d042a002a3ede10f19a637815d87cdeecf6c9c

Transactions (5)

Coinbasefacfd08ee6d644…f4fcbdef431341

1 in → 15 out9.3400 XPM573 B

AZwyMUeE…rxMQeLU7 AR13RD7s…sfkxQZ92 AFutDVqJ…TJTJj6UF AdKEgJo4…p6sjthXW AMypZdXS…5jJKu8wP

fda506ac82a899…4bc8fc3d524145

1 in → 2 out8.3714 XPM227 B

ALnRUEK1…jmoeSXLc AHAqHTyN…qgKusJNy

f4060502661d0a…aa9f4c34c30da3

1 in → 2 out8.1542 XPM225 B

AJPKZZv4…xpUJmLju AWXzbV5h…w7rY3AD3

735989a2d8b268…bb7a8d4288ca39

1 in → 2 out7.3614 XPM226 B

AGUiHrXX…99nzH74G ALzSptzK…ma9GAekm

747d856949a795…70d13ade089c4d

1 in → 2 out8.2033 XPM227 B

ASXAsx41…FDtznkgH AUu3NL5e…X1dNCtL1

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.

2.512 × 10⁹⁵(96-digit number)

25125740099087696813…01809868313617337599

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

2.512 × 10⁹⁵(96-digit number)

25125740099087696813…01809868313617337599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.512 × 10⁹⁵(96-digit number)

25125740099087696813…01809868313617337601

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

5.025 × 10⁹⁵(96-digit number)

50251480198175393627…03619736627234675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.025 × 10⁹⁵(96-digit number)

50251480198175393627…03619736627234675201

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

1.005 × 10⁹⁶(97-digit number)

10050296039635078725…07239473254469350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.005 × 10⁹⁶(97-digit number)

10050296039635078725…07239473254469350401

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

2.010 × 10⁹⁶(97-digit number)

20100592079270157451…14478946508938700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.010 × 10⁹⁶(97-digit number)

20100592079270157451…14478946508938700801

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

4.020 × 10⁹⁶(97-digit number)

40201184158540314902…28957893017877401599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.020 × 10⁹⁶(97-digit number)

40201184158540314902…28957893017877401601

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 #355,602

Cookie Preferences