Block #654,089

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/29/2014, 11:33:03 PM · Difficulty 10.9552 · 6,140,098 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5a4a7a95526c56c3e99376c1ae3d366e57679cff34e3d5f0c13029b3e1abb4cf

View on Chainz ↗

Height

#654,089

Difficulty

10.955170

Transactions

Size

110.26 KB

Version

Bits

0af48601

Nonce

1,028,082,191

Timestamp

7/29/2014, 11:33:03 PM

Confirmations

6,140,098

Merkle Root

5eeee066700ec40a5f5a2288b05d668f4e3930b0b361a49b31d168a669000ce9

Transactions (4)

Coinbase492cb12b711426…58daa998d3e2e2

1 in → 1 out9.4600 XPM116 B

ANSXnLY2…Sd25TjkD

bafb47777caf07…4e41444f84290c

253 in → 1 out500.0000 XPM36.62 KB

AUE5QneS…bDZqwQ1J

059b3a9f468967…fe1cd9f8499938

253 in → 2 out500.0100 XPM36.65 KB

APk31pKR…zZYLgvuf AUE5QneS…bDZqwQ1J

e87c9d4d5e4e71…94b3d5dd4341d4

254 in → 2 out500.0100 XPM36.80 KB

AUE5QneS…bDZqwQ1J AUEsdp9u…iBVVGJxi

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.

6.478 × 10⁹⁹(100-digit number)

64789435077475527544…23514011738354063359

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

6.478 × 10⁹⁹(100-digit number)

64789435077475527544…23514011738354063359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.478 × 10⁹⁹(100-digit number)

64789435077475527544…23514011738354063361

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

1.295 × 10¹⁰⁰(101-digit number)

12957887015495105508…47028023476708126719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.295 × 10¹⁰⁰(101-digit number)

12957887015495105508…47028023476708126721

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

2.591 × 10¹⁰⁰(101-digit number)

25915774030990211017…94056046953416253439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.591 × 10¹⁰⁰(101-digit number)

25915774030990211017…94056046953416253441

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

5.183 × 10¹⁰⁰(101-digit number)

51831548061980422035…88112093906832506879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.183 × 10¹⁰⁰(101-digit number)

51831548061980422035…88112093906832506881

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

1.036 × 10¹⁰¹(102-digit number)

10366309612396084407…76224187813665013759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.036 × 10¹⁰¹(102-digit number)

10366309612396084407…76224187813665013761

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

2.073 × 10¹⁰¹(102-digit number)

20732619224792168814…52448375627330027519

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