Block #83,865

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 10:40:24 AM · Difficulty 9.2708 · 6,710,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d896ae82dfdfbddd20eb329f27e4f23d02782e19268c5ce1065f645fa4c19547

View on Chainz ↗

Height

#83,865

Difficulty

9.270827

Transactions

Size

1.83 KB

Version

Bits

094554f3

Nonce

372

Timestamp

7/26/2013, 10:40:24 AM

Confirmations

6,710,532

Mined by

⛏️ P2SHASBsrqAfgGiPTfS9NW3hgsYbwPaom6miy1

Merkle Root

a6656d87f7d3c934543d927528f04805ad5567de0aa15e02c30cdbf698e7b5ed

Transactions (2)

Coinbase3cd35bf399157c…e6c15ca9f3d038

1 in → 1 out11.6400 XPM110 B

ASBsrqAf…aom6miy1

6428f4b602a3ff…bf94027a32b122

11 in → 1 out15.7300 XPM1.63 KB

AbNGMc8u…1U1JDfKe

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.

8.706 × 10¹⁰⁶(107-digit number)

87062226974060127693…68764983985760522389

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

8.706 × 10¹⁰⁶(107-digit number)

87062226974060127693…68764983985760522389

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.706 × 10¹⁰⁶(107-digit number)

87062226974060127693…68764983985760522391

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

1.741 × 10¹⁰⁷(108-digit number)

17412445394812025538…37529967971521044779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.741 × 10¹⁰⁷(108-digit number)

17412445394812025538…37529967971521044781

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

3.482 × 10¹⁰⁷(108-digit number)

34824890789624051077…75059935943042089559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.482 × 10¹⁰⁷(108-digit number)

34824890789624051077…75059935943042089561

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

6.964 × 10¹⁰⁷(108-digit number)

69649781579248102154…50119871886084179119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.964 × 10¹⁰⁷(108-digit number)

69649781579248102154…50119871886084179121

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

1.392 × 10¹⁰⁸(109-digit number)

13929956315849620430…00239743772168358239

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