Block #366,608

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2014, 12:31:41 PM · Difficulty 10.4331 · 6,435,943 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91fd049eb63aa0fd584d9e5d93a5f4f55badc28efe46238bf80df98abafbde9d

View on Chainz ↗

Height

#366,608

Difficulty

10.433087

Transactions

Size

1.84 KB

Version

Bits

0a6edecb

Nonce

3,859

Timestamp

1/19/2014, 12:31:41 PM

Confirmations

6,435,943

Mined by

AM4c6u8dYeQBkdo3RbtZ8WqY8DwUNSLEd4

Merkle Root

8acd35b22cccd46cdb6590f7f2a7c7eb7f08f26ea3dfb990abfae86f0cfaa173

Transactions (5)

Coinbaseac6596e3b4b9ff…efa01acca35887

1 in → 20 out9.2100 XPM743 B

AM4c6u8d…wUNSLEd4 AFutDVqJ…TJTJj6UF AKw4SCJo…8cHCpEcC AczyTBWn…bEQQj33u AMHMrUuK…jgEj6HLr

ff0f1d36a53fcb…113e407129845c

2 in → 2 out12.3216 XPM375 B

AY4uM53e…yee8uDKH APr4LciU…4c2EGouk

af6aa5493ce22b…da4a62d3069a40

1 in → 2 out6.1476 XPM225 B

Ab3Atk3t…w9zDbAwm ATrnVjXT…qGNzR5tU

81c790dc3cc04a…92cbe460817731

1 in → 2 out6.1540 XPM226 B

ALwCwRnU…xMuMZTXd AMU8nEj9…Eo32pqxr

d5ab5c1c70722a…c536bb1f74f063

1 in → 2 out4.6837 XPM227 B

ALe3Qn3m…pixEYdAc AarwrubJ…F3UoA6R1

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.

5.844 × 10⁹⁴(95-digit number)

58442104272077133454…12286357555068426959

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

5.844 × 10⁹⁴(95-digit number)

58442104272077133454…12286357555068426959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.844 × 10⁹⁴(95-digit number)

58442104272077133454…12286357555068426961

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

1.168 × 10⁹⁵(96-digit number)

11688420854415426690…24572715110136853919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.168 × 10⁹⁵(96-digit number)

11688420854415426690…24572715110136853921

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

2.337 × 10⁹⁵(96-digit number)

23376841708830853381…49145430220273707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.337 × 10⁹⁵(96-digit number)

23376841708830853381…49145430220273707841

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

4.675 × 10⁹⁵(96-digit number)

46753683417661706763…98290860440547415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.675 × 10⁹⁵(96-digit number)

46753683417661706763…98290860440547415681

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

9.350 × 10⁹⁵(96-digit number)

93507366835323413527…96581720881094831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.350 × 10⁹⁵(96-digit number)

93507366835323413527…96581720881094831361

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