Block #534,481

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/10/2014, 8:39:46 AM · Difficulty 10.9020 · 6,281,654 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6116eea0ffa0752bead99f45949d33346d3b2dc97bed615357594662aeae821

View on Chainz ↗

Height

#534,481

Difficulty

10.901978

Transactions

Size

1.57 KB

Version

Bits

0ae6e80c

Nonce

7,710

Timestamp

5/10/2014, 8:39:46 AM

Confirmations

6,281,654

Mined by

⛏️ 'QAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

8a63f86c7ab06b0eae00540c34aaf71121e9f75d88c2f4475630acccbc0b5e6c

Transactions (4)

Coinbase5caa715d83cbe0…739cbcdbcc51b3

1 in → 14 out8.4300 XPM539 B

AGz9gyZW…bo8NYQpw AXh3bnHa…j7qFoCbE AbPcCMg4…719q6mAX AMW1p9oT…2TzdaZxH AUFKXvnz…342ApNcm

ed25d7b9cf550e…0c187e7b77f802

2 in → 2 out12.0625 XPM376 B

Aa5bXeg1…zEXQ7Y2H ARvtnwog…L3A5gqKF

6089eee9ac2653…56358f753f2373

1 in → 2 out4.2228 XPM226 B

Abi8nFbt…bkDhGPuE AQh8TJPd…e2DrjJBi

41d35cf09c3977…cb0e813d4ab560

2 in → 2 out1.2741 XPM373 B

AbsdS8da…Q4DT3aCf AG8u7ddV…cU5QJSqk

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.

1.058 × 10⁹⁷(98-digit number)

10583966319988582973…30906898145031101439

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

1.058 × 10⁹⁷(98-digit number)

10583966319988582973…30906898145031101439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.058 × 10⁹⁷(98-digit number)

10583966319988582973…30906898145031101441

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

2.116 × 10⁹⁷(98-digit number)

21167932639977165947…61813796290062202879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.116 × 10⁹⁷(98-digit number)

21167932639977165947…61813796290062202881

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

4.233 × 10⁹⁷(98-digit number)

42335865279954331894…23627592580124405759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.233 × 10⁹⁷(98-digit number)

42335865279954331894…23627592580124405761

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

8.467 × 10⁹⁷(98-digit number)

84671730559908663788…47255185160248811519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.467 × 10⁹⁷(98-digit number)

84671730559908663788…47255185160248811521

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

1.693 × 10⁹⁸(99-digit number)

16934346111981732757…94510370320497623039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.693 × 10⁹⁸(99-digit number)

16934346111981732757…94510370320497623041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.386 × 10⁹⁸(99-digit number)

33868692223963465515…89020740640995246079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #534,481

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