Block #569,666

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/31/2014, 7:22:30 AM · Difficulty 10.9648 · 6,257,563 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9db5eaa7eda5d56fd513dfb17bd6625a81b009ec8c531ab99a95be0767b2f4e8

View on Chainz ↗

Height

#569,666

Difficulty

10.964752

Transactions

Size

731 B

Version

Bits

0af6fa01

Nonce

391,020,809

Timestamp

5/31/2014, 7:22:30 AM

Confirmations

6,257,563

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e36a5dbfa0131c5b1eb05a68e566cdd3d943fb105d5d1c77779df5ccf8f76429

Transactions (2)

Coinbase62c5e95b5d8dc0…f75c126b6ec2f3

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

1c8c5f029240d4…f3c0b0cb9eaab5

3 in → 2 out299.9100 XPM523 B

ARkumKR4…hB2QFDKB APcHQSmu…FMZFh8K4

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.

1.941 × 10⁹⁹(100-digit number)

19419924473396214787…55965739208836577279

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

1.941 × 10⁹⁹(100-digit number)

19419924473396214787…55965739208836577279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.941 × 10⁹⁹(100-digit number)

19419924473396214787…55965739208836577281

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

3.883 × 10⁹⁹(100-digit number)

38839848946792429575…11931478417673154559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.883 × 10⁹⁹(100-digit number)

38839848946792429575…11931478417673154561

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

7.767 × 10⁹⁹(100-digit number)

77679697893584859151…23862956835346309119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.767 × 10⁹⁹(100-digit number)

77679697893584859151…23862956835346309121

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

1.553 × 10¹⁰⁰(101-digit number)

15535939578716971830…47725913670692618239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.553 × 10¹⁰⁰(101-digit number)

15535939578716971830…47725913670692618241

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

3.107 × 10¹⁰⁰(101-digit number)

31071879157433943660…95451827341385236479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.107 × 10¹⁰⁰(101-digit number)

31071879157433943660…95451827341385236481

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

6.214 × 10¹⁰⁰(101-digit number)

62143758314867887321…90903654682770472959

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 #569,666

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