Block #82,919

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 6:44:00 PM · Difficulty 9.2727 · 6,712,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

557fdf007404db8b6ba28ec20e9a33dca95b454d68b54353ae06b7ab07c48421

View on Chainz ↗

Height

#82,919

Difficulty

9.272694

Transactions

Size

787 B

Version

Bits

0945cf49

Nonce

117,948

Timestamp

7/25/2013, 6:44:00 PM

Confirmations

6,712,131

Mined by

⛏️ P2SHAWuDuxGXKEXYj7RYhx64EdJKzBtLDpHWp7

Merkle Root

a46d2d06bb24a9c0af19c58b1b4a549c48e246ef4c836c6ab421728a375c0dcc

Transactions (4)

Coinbased531a707ff20b9…f94b3cc23f401e

1 in → 1 out11.6400 XPM109 B

AWuDuxGX…tLDpHWp7

ac827d3da5fbb9…b852292775c548

2 in → 1 out23.4000 XPM271 B

APxYM4np…KRuxb7a6

7c9b43313affe6…81d29e3decbe5d

1 in → 1 out11.7100 XPM158 B

AcS31cBK…Dmi7rdMj

3b220908cc2632…ca1f82321a8e3f

1 in → 1 out11.7000 XPM159 B

AcS31cBK…Dmi7rdMj

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.

2.542 × 10⁹⁵(96-digit number)

25423711873519178769…27147156984020552099

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

2.542 × 10⁹⁵(96-digit number)

25423711873519178769…27147156984020552099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.542 × 10⁹⁵(96-digit number)

25423711873519178769…27147156984020552101

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

5.084 × 10⁹⁵(96-digit number)

50847423747038357539…54294313968041104199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.084 × 10⁹⁵(96-digit number)

50847423747038357539…54294313968041104201

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

1.016 × 10⁹⁶(97-digit number)

10169484749407671507…08588627936082208399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.016 × 10⁹⁶(97-digit number)

10169484749407671507…08588627936082208401

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

2.033 × 10⁹⁶(97-digit number)

20338969498815343015…17177255872164416799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.033 × 10⁹⁶(97-digit number)

20338969498815343015…17177255872164416801

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

4.067 × 10⁹⁶(97-digit number)

40677938997630686031…34354511744328833599

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