Block #83,335

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 2:12:35 AM · Difficulty 9.2676 · 6,720,196 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f97acaa1bd4544306a4e1578676edbf9bdc906112db2c8b36e5bb3c85a3be7a

View on Chainz ↗

Height

#83,335

Difficulty

9.267599

Transactions

Size

204 B

Version

Bits

09448162

Nonce

34,654

Timestamp

7/26/2013, 2:12:35 AM

Confirmations

6,720,196

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

0824fc18325bdc3faa73fa4eb98a5cb92bd21ac72a420969df6ee3e470167151

Transactions (1)

Coinbase0824fc18325bdc…6ee3e470167151

1 in → 1 out11.6300 XPM109 B

AcuJraLT…Y66BS47Q

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.

4.098 × 10¹⁰⁵(106-digit number)

40980082569382167704…83086869974210365119

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

4.098 × 10¹⁰⁵(106-digit number)

40980082569382167704…83086869974210365119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.098 × 10¹⁰⁵(106-digit number)

40980082569382167704…83086869974210365121

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

8.196 × 10¹⁰⁵(106-digit number)

81960165138764335408…66173739948420730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.196 × 10¹⁰⁵(106-digit number)

81960165138764335408…66173739948420730241

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

1.639 × 10¹⁰⁶(107-digit number)

16392033027752867081…32347479896841460479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.639 × 10¹⁰⁶(107-digit number)

16392033027752867081…32347479896841460481

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

3.278 × 10¹⁰⁶(107-digit number)

32784066055505734163…64694959793682920959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.278 × 10¹⁰⁶(107-digit number)

32784066055505734163…64694959793682920961

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

6.556 × 10¹⁰⁶(107-digit number)

65568132111011468326…29389919587365841919

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