Block #663,557

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/5/2014, 9:06:43 AM · Difficulty 10.9577 · 6,145,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf542a6ce255ca9f4437e378bcd0bbcfb5308e4cce54d124dbd8e4216c7b97c1

View on Chainz ↗

Height

#663,557

Difficulty

10.957671

Transactions

Size

3.58 KB

Version

Bits

0af529e8

Nonce

35,750,926

Timestamp

8/5/2014, 9:06:43 AM

Confirmations

6,145,311

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ec0510c6384bc2f8331702c149887979dd3639c868c6cba4c8ace1aa3bb4c3dd

Transactions (5)

Coinbasedfdbac8ca63d9e…30f135216a5656

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

cecd8058153031…87df957d1eccf0

7 in → 2 out50.1608 XPM1.09 KB

AcrRunCM…Tu2stnTQ AcuimsJt…T3cV7pg6

8e04a7f2e1ca65…ebcdeffbf47b81

3 in → 2 out20.8204 XPM521 B

AaU9J1Lk…4e47uLfq APKtruGg…H5mBtKxW

42932e64038f44…773ab3dfb5f37e

10 in → 2 out50.3126 XPM1.52 KB

AWi9bZTK…5YAbyMqs AG37KGjd…coYLfn6r

fcdda0cc762da6…50f5956f0fd8af

1 in → 3 out4.2612 XPM260 B

AeKNrjNj…1NEq95Ta AQtKyTYr…UjAihQdg AL9UZuKj…g3Q3eciV

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.

2.289 × 10⁹⁹(100-digit number)

22899653865246868264…92311976239891742719

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

2.289 × 10⁹⁹(100-digit number)

22899653865246868264…92311976239891742719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.289 × 10⁹⁹(100-digit number)

22899653865246868264…92311976239891742721

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

4.579 × 10⁹⁹(100-digit number)

45799307730493736528…84623952479783485439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.579 × 10⁹⁹(100-digit number)

45799307730493736528…84623952479783485441

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

9.159 × 10⁹⁹(100-digit number)

91598615460987473056…69247904959566970879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.159 × 10⁹⁹(100-digit number)

91598615460987473056…69247904959566970881

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

1.831 × 10¹⁰⁰(101-digit number)

18319723092197494611…38495809919133941759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.831 × 10¹⁰⁰(101-digit number)

18319723092197494611…38495809919133941761

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

3.663 × 10¹⁰⁰(101-digit number)

36639446184394989222…76991619838267883519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.663 × 10¹⁰⁰(101-digit number)

36639446184394989222…76991619838267883521

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

7.327 × 10¹⁰⁰(101-digit number)

73278892368789978445…53983239676535767039

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 #663,557

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