Block #1,588,392

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2016, 10:07:33 AM · Difficulty 10.6507 · 5,238,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ceb9b2d4d9b9564046503e9c507c84d9e0c028f49e78d04e47eed21300d22669

View on Chainz ↗

Height

#1,588,392

Difficulty

10.650698

Transactions

Size

1.21 KB

Version

Bits

0aa69428

Nonce

732,989,612

Timestamp

5/17/2016, 10:07:33 AM

Confirmations

5,238,374

Mined by

⛏️ P2SHAXcjaSBciR9MHAPE2RXQRbWB393x77nEy2

Merkle Root

9e3bba029ee5971a60aada791ce1c276bf2fac80781d6739b047280673ebb4b6

Transactions (2)

Coinbase4fa3e85066b23d…37b2488555fffb

1 in → 1 out8.8200 XPM109 B

AXcjaSBc…3x77nEy2

fe65f056758176…48dd111e727430

1 in → 26 out18.7102 XPM1.02 KB

AcJzrqoN…sC5CU1nw AS7EhQy8…svFmz7yp AeP3TFaN…PEbFkY3m AafCLqqv…EeFxBfBr AVvPsNGi…95jd1dTR

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.

6.672 × 10⁹⁴(95-digit number)

66725758597791555860…76012192297540587319

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

6.672 × 10⁹⁴(95-digit number)

66725758597791555860…76012192297540587319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.672 × 10⁹⁴(95-digit number)

66725758597791555860…76012192297540587321

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

1.334 × 10⁹⁵(96-digit number)

13345151719558311172…52024384595081174639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.334 × 10⁹⁵(96-digit number)

13345151719558311172…52024384595081174641

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

2.669 × 10⁹⁵(96-digit number)

26690303439116622344…04048769190162349279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.669 × 10⁹⁵(96-digit number)

26690303439116622344…04048769190162349281

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

5.338 × 10⁹⁵(96-digit number)

53380606878233244688…08097538380324698559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.338 × 10⁹⁵(96-digit number)

53380606878233244688…08097538380324698561

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

1.067 × 10⁹⁶(97-digit number)

10676121375646648937…16195076760649397119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.067 × 10⁹⁶(97-digit number)

10676121375646648937…16195076760649397121

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 #1,588,392

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