Block #594,665

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/19/2014, 4:53:04 PM · Difficulty 10.9382 · 6,222,450 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

47a6b5ea8c60ef81e1150d996aabb516e1572d74994f43f8ea4e4fb067ef38dc

View on Chainz ↗

Height

#594,665

Difficulty

10.938225

Transactions

Size

434 B

Version

Bits

0af02f82

Nonce

72,161,078

Timestamp

6/19/2014, 4:53:04 PM

Confirmations

6,222,450

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4cb99040a3e02b67fcc9c14b4589ae34b9d6fa25dc22a32c5773af88c80c5877

Transactions (2)

Coinbasec5782e2620733d…42a4c2dd38bf4b

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

8330f5738786f3…be07561d39bb5f

1 in → 2 out6.0099 XPM226 B

ATb2V6U1…cAx9fkWD AcdKfoeT…wXd4Zxk3

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.

1.300 × 10⁹⁹(100-digit number)

13005311976766701643…66421604297902557439

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

1.300 × 10⁹⁹(100-digit number)

13005311976766701643…66421604297902557439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.300 × 10⁹⁹(100-digit number)

13005311976766701643…66421604297902557441

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

2.601 × 10⁹⁹(100-digit number)

26010623953533403286…32843208595805114879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.601 × 10⁹⁹(100-digit number)

26010623953533403286…32843208595805114881

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

5.202 × 10⁹⁹(100-digit number)

52021247907066806572…65686417191610229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.202 × 10⁹⁹(100-digit number)

52021247907066806572…65686417191610229761

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

1.040 × 10¹⁰⁰(101-digit number)

10404249581413361314…31372834383220459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.040 × 10¹⁰⁰(101-digit number)

10404249581413361314…31372834383220459521

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

2.080 × 10¹⁰⁰(101-digit number)

20808499162826722629…62745668766440919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.080 × 10¹⁰⁰(101-digit number)

20808499162826722629…62745668766440919041

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

4.161 × 10¹⁰⁰(101-digit number)

41616998325653445258…25491337532881838079

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 #594,665

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