Block #3,463,859

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2019, 10:55:31 AM · Difficulty 10.9788 · 3,380,916 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6085f9bb9089c4bf44a38c0ea2dde394285e423e58223b5d24160e2e08e761fe

View on Chainz ↗

Height

#3,463,859

Difficulty

10.978752

Transactions

Size

1.58 KB

Version

Bits

0afa8f79

Nonce

411,882,517

Timestamp

12/6/2019, 10:55:31 AM

Confirmations

3,380,916

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

c7d8dcb6e691b5a67e265ade3fbbccf93b4266cb6416cef694249e8ec72de553

Transactions (2)

Coinbase7f43d6eca07189…4d776147609701

1 in → 1 out8.3000 XPM110 B

AXfJqzUb…HXeXmjMz

167eaf8d69ab24…2e2ab5eabd8cc1

9 in → 2 out1681.1390 XPM1.38 KB

AP2ikm3r…2qJRNrn6 AJNqcuWW…LXrv2pRL

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.

8.346 × 10⁹⁴(95-digit number)

83464398990352212906…94655891302038367999

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

8.346 × 10⁹⁴(95-digit number)

83464398990352212906…94655891302038367999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.346 × 10⁹⁴(95-digit number)

83464398990352212906…94655891302038368001

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

1.669 × 10⁹⁵(96-digit number)

16692879798070442581…89311782604076735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.669 × 10⁹⁵(96-digit number)

16692879798070442581…89311782604076736001

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

3.338 × 10⁹⁵(96-digit number)

33385759596140885162…78623565208153471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.338 × 10⁹⁵(96-digit number)

33385759596140885162…78623565208153472001

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

6.677 × 10⁹⁵(96-digit number)

66771519192281770325…57247130416306943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.677 × 10⁹⁵(96-digit number)

66771519192281770325…57247130416306944001

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

1.335 × 10⁹⁶(97-digit number)

13354303838456354065…14494260832613887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.335 × 10⁹⁶(97-digit number)

13354303838456354065…14494260832613888001

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 #3,463,859

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