Block #1,589,682

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/18/2016, 7:08:21 AM · Difficulty 10.6527 · 5,252,798 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0b0f4e65436699cfd81dabd9214c2698a6f1a0833b2ca654400b0696e3dbf9c

View on Chainz ↗

Height

#1,589,682

Difficulty

10.652746

Transactions

Size

1.64 KB

Version

Bits

0aa71a5f

Nonce

169,549,381

Timestamp

5/18/2016, 7:08:21 AM

Confirmations

5,252,798

Mined by

⛏️ P2SHAUc887AKZ686dXVSocboCvooAt1wDWnCp7

Merkle Root

ed76d2b533d3756ce60b74efc563c2745070cb219192db84fc34c3a2e1749b3d

Transactions (2)

Coinbase294d66d379b3e8…dc472df884191d

1 in → 1 out8.8200 XPM109 B

AUc887AK…1wDWnCp7

b7f484374abe16…7be7738b15823a

1 in → 39 out187.5516 XPM1.45 KB

AZb72Xpi…jMwjS9yX AMJsR7Zo…MJV42TZM AQK5pf1K…VCfFttc3 AbqDvKJf…Xup3v4n2 AGf2Yjrb…ma7pXipe

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.

4.124 × 10⁹⁵(96-digit number)

41249888020689031974…50399761732077880319

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

4.124 × 10⁹⁵(96-digit number)

41249888020689031974…50399761732077880319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.124 × 10⁹⁵(96-digit number)

41249888020689031974…50399761732077880321

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

8.249 × 10⁹⁵(96-digit number)

82499776041378063949…00799523464155760639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.249 × 10⁹⁵(96-digit number)

82499776041378063949…00799523464155760641

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

1.649 × 10⁹⁶(97-digit number)

16499955208275612789…01599046928311521279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.649 × 10⁹⁶(97-digit number)

16499955208275612789…01599046928311521281

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

3.299 × 10⁹⁶(97-digit number)

32999910416551225579…03198093856623042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.299 × 10⁹⁶(97-digit number)

32999910416551225579…03198093856623042561

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

6.599 × 10⁹⁶(97-digit number)

65999820833102451159…06396187713246085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.599 × 10⁹⁶(97-digit number)

65999820833102451159…06396187713246085121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,589,682

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