Block #183,095

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 6:47:03 PM · Difficulty 9.8580 · 6,621,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cbb77a7d0c4ee9c0ccbb74bded2f7af5a8b04f70257d418cc0ca2729689994a2

View on Chainz ↗

Height

#183,095

Difficulty

9.857979

Transactions

Size

878 B

Version

Bits

09dba47e

Nonce

5,754

Timestamp

9/27/2013, 6:47:03 PM

Confirmations

6,621,807

Mined by

⛏️ P2SHAZeU2g2L3DVc23NKBGDPLkL6PBm694WpGV

Merkle Root

51585e81bf0839dc03874bd333b9a114594f1c84d58baf8d9ce53a927cb65d8e

Transactions (4)

Coinbase99134e8adcbb2d…6ff6886aafb8d8

1 in → 1 out10.3000 XPM109 B

AZeU2g2L…m694WpGV

38ef0a0925c8c8…5021da9967cf7e

1 in → 2 out8.2263 XPM227 B

AcW8LBZL…U9Rn1wL4 AKCvAf81…bmir7MN9

6ba1f12ce56470…4dd707ad8dfb06

1 in → 2 out6.1832 XPM226 B

AXwKKGcU…yK2w3TwR AGT2PLqq…jY2AiyXN

d31b1ff37410d3…7627e3f67769a3

1 in → 2 out4.1903 XPM227 B

AMNXrRDB…YdQiNMLb AUfBNY3y…Mm2UYiNj

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.

1.888 × 10⁹²(93-digit number)

18884046938412125568…50813004908349480959

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

1.888 × 10⁹²(93-digit number)

18884046938412125568…50813004908349480959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.888 × 10⁹²(93-digit number)

18884046938412125568…50813004908349480961

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

3.776 × 10⁹²(93-digit number)

37768093876824251136…01626009816698961919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.776 × 10⁹²(93-digit number)

37768093876824251136…01626009816698961921

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

7.553 × 10⁹²(93-digit number)

75536187753648502273…03252019633397923839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.553 × 10⁹²(93-digit number)

75536187753648502273…03252019633397923841

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

1.510 × 10⁹³(94-digit number)

15107237550729700454…06504039266795847679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.510 × 10⁹³(94-digit number)

15107237550729700454…06504039266795847681

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

3.021 × 10⁹³(94-digit number)

30214475101459400909…13008078533591695359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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