Block #355,856

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 10:11:27 AM · Difficulty 10.3654 · 6,456,790 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

494d9ea8fceac565bb19b3fafdb2a8f894bf133a96356ab088397fd69b81f508

View on Chainz ↗

Height

#355,856

Difficulty

10.365394

Transactions

Size

3.97 KB

Version

Bits

0a5d8a72

Nonce

3,574

Timestamp

1/12/2014, 10:11:27 AM

Confirmations

6,456,790

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

29eb41772cd6bbc64149a836992cbea8afbb1613bafaf7c2ca7e3de5d9aeef8a

Transactions (5)

Coinbase4b674ce1ee464a…eaac03f0feab94

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

8c4fc0820740e8…363773cab733a2

21 in → 2 out160.4856 XPM3.11 KB

ANWCrwhY…QSVrQAGu ARRAPAMf…UfPM2VqG

9a369a54413db9…f59fc1e77c3ed1

1 in → 2 out6.3421 XPM226 B

ATVRyzmg…cNvu3WAP Aahfq3LG…yuWTsv5R

4b19aa33c3ba8d…a8940241dd1019

1 in → 2 out5.1557 XPM226 B

AKGV6suz…nADaeuiS AduqHWhc…1sKqeZgm

0057633fd4f96e…733def2d21dc29

1 in → 2 out5.0693 XPM226 B

APhyxg3g…LNqfRJSZ AdpkvdMC…k8bEC2ts

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.

3.073 × 10⁹⁵(96-digit number)

30739444254607556372…43719639848680563199

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

3.073 × 10⁹⁵(96-digit number)

30739444254607556372…43719639848680563199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.073 × 10⁹⁵(96-digit number)

30739444254607556372…43719639848680563201

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

6.147 × 10⁹⁵(96-digit number)

61478888509215112745…87439279697361126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.147 × 10⁹⁵(96-digit number)

61478888509215112745…87439279697361126401

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

1.229 × 10⁹⁶(97-digit number)

12295777701843022549…74878559394722252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.229 × 10⁹⁶(97-digit number)

12295777701843022549…74878559394722252801

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

2.459 × 10⁹⁶(97-digit number)

24591555403686045098…49757118789444505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.459 × 10⁹⁶(97-digit number)

24591555403686045098…49757118789444505601

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

4.918 × 10⁹⁶(97-digit number)

49183110807372090196…99514237578889011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.918 × 10⁹⁶(97-digit number)

49183110807372090196…99514237578889011201

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 #355,856

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