Block #82,161

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 5:48:15 AM · Difficulty 9.2748 · 6,725,709 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

90bd8893c346fe4ae2a0eac23f7f1908e5bdf3c8b6d9d91a3a26663aef660ca2

View on Chainz ↗

Height

#82,161

Difficulty

9.274847

Transactions

Size

205 B

Version

Bits

09465c63

Nonce

38,565

Timestamp

7/25/2013, 5:48:15 AM

Confirmations

6,725,709

Mined by

⛏️ P2SHAbmC177FbWsA3xjDrM8MdR2hvjpomdGgdX

Merkle Root

f975b263adb147fc37377f8013b9a086b73945c9ca02a1c539131df9ea6d497b

Transactions (1)

Coinbasef975b263adb147…131df9ea6d497b

1 in → 1 out11.6100 XPM109 B

AbmC177F…pomdGgdX

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.

1.872 × 10¹⁰⁹(110-digit number)

18727439319210848215…10558444131392802489

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

1.872 × 10¹⁰⁹(110-digit number)

18727439319210848215…10558444131392802489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.872 × 10¹⁰⁹(110-digit number)

18727439319210848215…10558444131392802491

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

3.745 × 10¹⁰⁹(110-digit number)

37454878638421696431…21116888262785604979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.745 × 10¹⁰⁹(110-digit number)

37454878638421696431…21116888262785604981

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

7.490 × 10¹⁰⁹(110-digit number)

74909757276843392862…42233776525571209959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.490 × 10¹⁰⁹(110-digit number)

74909757276843392862…42233776525571209961

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

1.498 × 10¹¹⁰(111-digit number)

14981951455368678572…84467553051142419919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.498 × 10¹¹⁰(111-digit number)

14981951455368678572…84467553051142419921

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

2.996 × 10¹¹⁰(111-digit number)

29963902910737357145…68935106102284839839

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

Block #82,161

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