Block #355,474

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 4:14:57 AM · Difficulty 10.3601 · 6,471,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fbd1817a4582774511b1c0c3399353f2bf132a9a3641063d9430d6a017ecf33b

View on Chainz ↗

Height

#355,474

Difficulty

10.360089

Transactions

Size

1.05 KB

Version

Bits

0a5c2ece

Nonce

8,045

Timestamp

1/12/2014, 4:14:57 AM

Confirmations

6,471,076

Mined by

⛏️ laRJAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

bc12083b83248e9929293b1727e2710fcd54a2534943a6bbf67a38dc1ac28259

Transactions (1)

Coinbasebc12083b83248e…7a38dc1ac28259

1 in → 27 out9.3000 XPM981 B

Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AUnkFe8H…fvenjA4X AQvZBsUo…hppgRZTJ AMiJebLB…rK2iN8iS

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.

5.463 × 10⁹⁴(95-digit number)

54635938975263379254…89065370715689720639

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

5.463 × 10⁹⁴(95-digit number)

54635938975263379254…89065370715689720639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.463 × 10⁹⁴(95-digit number)

54635938975263379254…89065370715689720641

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

1.092 × 10⁹⁵(96-digit number)

10927187795052675850…78130741431379441279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.092 × 10⁹⁵(96-digit number)

10927187795052675850…78130741431379441281

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

2.185 × 10⁹⁵(96-digit number)

21854375590105351701…56261482862758882559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.185 × 10⁹⁵(96-digit number)

21854375590105351701…56261482862758882561

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

4.370 × 10⁹⁵(96-digit number)

43708751180210703403…12522965725517765119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.370 × 10⁹⁵(96-digit number)

43708751180210703403…12522965725517765121

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

8.741 × 10⁹⁵(96-digit number)

87417502360421406807…25045931451035530239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.741 × 10⁹⁵(96-digit number)

87417502360421406807…25045931451035530241

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 #355,474

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