Block #359,732

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 11:45:44 PM · Difficulty 10.3894 · 6,465,205 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df9da2607295eb3d62b7fb7dac2c1cc142f81beb5f8bcdb9841233e7724a3cc1

View on Chainz ↗

Height

#359,732

Difficulty

10.389367

Transactions

Size

1014 B

Version

Bits

0a63ad86

Nonce

54,153

Timestamp

1/14/2014, 11:45:44 PM

Confirmations

6,465,205

Mined by

AMQC4aya4xubziAP8jJGG5nLpZc4ptxi3K

Merkle Root

1f70653d4b6995386ee85ddd5c4e147a6fcb077ac9817644f23e84df75f1efff

Transactions (2)

Coinbasecabbf9c973406f…2e433f4cf55299

1 in → 5 out9.2600 XPM233 B

AMQC4aya…c4ptxi3K AakJsGaf…CSFKrp9K AKMBvL7P…npwgm5sY ARpndEmc…Hg792kEk AJno7LX2…vo4wdWtY

08afd7b4891da4…9da330f7a32e58

3 in → 10 out28.0100 XPM691 B

AeKNrjNj…1NEq95Ta APrTf91F…Urxts9FM AHRDUnh4…89Qh8BeJ AW6J7sMt…T4Pi5rgv AQ8rAY3V…anzVDEuW

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.

5.279 × 10⁹³(94-digit number)

52796159055889277377…21405767931982120459

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

5.279 × 10⁹³(94-digit number)

52796159055889277377…21405767931982120459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.279 × 10⁹³(94-digit number)

52796159055889277377…21405767931982120461

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

1.055 × 10⁹⁴(95-digit number)

10559231811177855475…42811535863964240919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.055 × 10⁹⁴(95-digit number)

10559231811177855475…42811535863964240921

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

2.111 × 10⁹⁴(95-digit number)

21118463622355710951…85623071727928481839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.111 × 10⁹⁴(95-digit number)

21118463622355710951…85623071727928481841

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

4.223 × 10⁹⁴(95-digit number)

42236927244711421902…71246143455856963679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.223 × 10⁹⁴(95-digit number)

42236927244711421902…71246143455856963681

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

8.447 × 10⁹⁴(95-digit number)

84473854489422843804…42492286911713927359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.447 × 10⁹⁴(95-digit number)

84473854489422843804…42492286911713927361

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 #359,732

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