Block #436,951

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 11:08:45 PM · Difficulty 10.3592 · 6,380,771 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f113f9683b799b176b1c39c67e267557c55dfac2b70d3d1f98b2c024b5733b4

View on Chainz ↗

Height

#436,951

Difficulty

10.359245

Transactions

Size

768 B

Version

Bits

0a5bf777

Nonce

13,045

Timestamp

3/9/2014, 11:08:45 PM

Confirmations

6,380,771

Mined by

⛏️ aSisAbmgKH5P9bbBkJqQUg2sQk61L7HJmmbL8k

Merkle Root

55e83818cdad750a9160db9b927f87cfe2ad92f818219828197d988d9a0f3dc9

Transactions (1)

Coinbase55e83818cdad75…7d988d9a0f3dc9

1 in → 18 out9.3000 XPM675 B

AbmgKH5P…HJmmbL8k AHqZtsfn…WrCGjM3J AGKhfQo2…h7fBXLX6 AScAzqGc…BZ6tV1vJ Aac9Hjdg…P4ktypc3

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.

1.341 × 10¹⁰¹(102-digit number)

13418705174018580913…39252496199454643199

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

1.341 × 10¹⁰¹(102-digit number)

13418705174018580913…39252496199454643199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.341 × 10¹⁰¹(102-digit number)

13418705174018580913…39252496199454643201

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

2.683 × 10¹⁰¹(102-digit number)

26837410348037161827…78504992398909286399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.683 × 10¹⁰¹(102-digit number)

26837410348037161827…78504992398909286401

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

5.367 × 10¹⁰¹(102-digit number)

53674820696074323655…57009984797818572799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.367 × 10¹⁰¹(102-digit number)

53674820696074323655…57009984797818572801

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

1.073 × 10¹⁰²(103-digit number)

10734964139214864731…14019969595637145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.073 × 10¹⁰²(103-digit number)

10734964139214864731…14019969595637145601

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

2.146 × 10¹⁰²(103-digit number)

21469928278429729462…28039939191274291199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.146 × 10¹⁰²(103-digit number)

21469928278429729462…28039939191274291201

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 #436,951

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