Block #582,596

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/9/2014, 7:29:58 PM · Difficulty 10.9595 · 6,234,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92599ce8d7418e0922eede9ec93c8b36811029c2be620322f1e05bc25b95bae5

View on Chainz ↗

Height

#582,596

Difficulty

10.959531

Transactions

Size

1.23 KB

Version

Bits

0af5a3d9

Nonce

227,342,351

Timestamp

6/9/2014, 7:29:58 PM

Confirmations

6,234,150

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5197daa29cfa29ec58acc52217ce54270d4a17045fbb2835c2cc1d347df67ec9

Transactions (5)

Coinbase11707dd985f88d…23653aec7b3b7e

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

558ac576e08fa1…3ffe54fc7ae435

2 in → 2 out11.7653 XPM376 B

AWJJtX3B…L7HrAhMH ASUbvGQ3…eWcvX9ZX

297a59110bee8b…e21710de30cdc4

1 in → 2 out5.7401 XPM226 B

AbPCaLQe…PaJTUokm AGdWVjRk…LFVsqCnK

f0c4943aea4252…7ae6617d161489

1 in → 2 out5.5146 XPM226 B

AQ4S8AtJ…Hzkvi1gQ ANfKsKrT…YwsZQ3Ty

e9431dc2b51b5d…c28e406a89119b

1 in → 2 out4.6987 XPM227 B

AcrhdUuL…U1PF5aTU AKV6QDPr…mY82NcbY

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.

6.162 × 10⁹⁸(99-digit number)

61627524211120227772…18356836124870360639

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

6.162 × 10⁹⁸(99-digit number)

61627524211120227772…18356836124870360639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.162 × 10⁹⁸(99-digit number)

61627524211120227772…18356836124870360641

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

1.232 × 10⁹⁹(100-digit number)

12325504842224045554…36713672249740721279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.232 × 10⁹⁹(100-digit number)

12325504842224045554…36713672249740721281

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

2.465 × 10⁹⁹(100-digit number)

24651009684448091109…73427344499481442559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.465 × 10⁹⁹(100-digit number)

24651009684448091109…73427344499481442561

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

4.930 × 10⁹⁹(100-digit number)

49302019368896182218…46854688998962885119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.930 × 10⁹⁹(100-digit number)

49302019368896182218…46854688998962885121

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

9.860 × 10⁹⁹(100-digit number)

98604038737792364436…93709377997925770239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.860 × 10⁹⁹(100-digit number)

98604038737792364436…93709377997925770241

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

1.972 × 10¹⁰⁰(101-digit number)

19720807747558472887…87418755995851540479

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 #582,596

Cookie Preferences