Block #366,282

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2014, 7:48:53 AM · Difficulty 10.4278 · 6,444,632 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a753183aa05cdbe5cd9679d9caa14b816f1edfa0c3b6a18756b372ff539878ab

View on Chainz ↗

Height

#366,282

Difficulty

10.427801

Transactions

Size

28.83 KB

Version

Bits

0a6d845b

Nonce

57,118

Timestamp

1/19/2014, 7:48:53 AM

Confirmations

6,444,632

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9214ae97199a385df496907674d4d9f66829520f18ad88a7b3a152cede08ec1a

Transactions (3)

Coinbase84d0081796dd9e…48c089879fc6e3

1 in → 1 out9.4900 XPM110 B

AeKNrjNj…1NEq95Ta

45d3b1b4408f1c…452b6941beed9b

62 in → 2 out20.9657 XPM9.03 KB

AZASNyVa…Mt22oZUx ATHh64cY…1yfxXkAQ

4bb52d2265c537…a4c83f9aee1cdd

135 in → 2 out56.0103 XPM19.60 KB

Aeg59DTc…kFBorQY5 ATa4KeiN…gVZsjZvB

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.

1.222 × 10⁹⁸(99-digit number)

12220628634616828599…65563695084937512489

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

1.222 × 10⁹⁸(99-digit number)

12220628634616828599…65563695084937512489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.222 × 10⁹⁸(99-digit number)

12220628634616828599…65563695084937512491

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

2.444 × 10⁹⁸(99-digit number)

24441257269233657199…31127390169875024979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.444 × 10⁹⁸(99-digit number)

24441257269233657199…31127390169875024981

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

4.888 × 10⁹⁸(99-digit number)

48882514538467314398…62254780339750049959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.888 × 10⁹⁸(99-digit number)

48882514538467314398…62254780339750049961

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

9.776 × 10⁹⁸(99-digit number)

97765029076934628797…24509560679500099919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.776 × 10⁹⁸(99-digit number)

97765029076934628797…24509560679500099921

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

1.955 × 10⁹⁹(100-digit number)

19553005815386925759…49019121359000199839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.955 × 10⁹⁹(100-digit number)

19553005815386925759…49019121359000199841

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 #366,282

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