Block #1,034,468

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2015, 5:30:45 AM · Difficulty 10.7466 · 5,799,306 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80d6672a0c3426672231dad11c60c333c5706237ef96695a46b48a8ba994ecdf

View on Chainz ↗

Height

#1,034,468

Difficulty

10.746600

Transactions

Size

242 B

Version

Bits

0abf2130

Nonce

2,952,103,397

Timestamp

4/27/2015, 5:30:45 AM

Confirmations

5,799,306

Mined by

⛏️ P2SHAUV3ZXsawxZuaXubcanNHw2sUMP3xQCbyH

Merkle Root

dcb5178774d1aebfd67f1279b4a86712dfee0a29f78499d28e9c4e275f886957

Transactions (1)

Coinbasedcb5178774d1ae…9c4e275f886957

1 in → 2 out8.6500 XPM152 B

AUV3ZXsa…P3xQCbyH ALPu3s2c…EJXLjVFh

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.

8.276 × 10⁹³(94-digit number)

82764836871745321300…11808648749193819009

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

8.276 × 10⁹³(94-digit number)

82764836871745321300…11808648749193819009

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.276 × 10⁹³(94-digit number)

82764836871745321300…11808648749193819011

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

1.655 × 10⁹⁴(95-digit number)

16552967374349064260…23617297498387638019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.655 × 10⁹⁴(95-digit number)

16552967374349064260…23617297498387638021

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

3.310 × 10⁹⁴(95-digit number)

33105934748698128520…47234594996775276039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.310 × 10⁹⁴(95-digit number)

33105934748698128520…47234594996775276041

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

6.621 × 10⁹⁴(95-digit number)

66211869497396257040…94469189993550552079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.621 × 10⁹⁴(95-digit number)

66211869497396257040…94469189993550552081

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

1.324 × 10⁹⁵(96-digit number)

13242373899479251408…88938379987101104159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.324 × 10⁹⁵(96-digit number)

13242373899479251408…88938379987101104161

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 #1,034,468

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