Block #82,515

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 11:48:07 AM · Difficulty 9.2740 · 6,712,869 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df5f2b4c768f69dea795668e9042ec926d68d10ca668794ab3fca4ef9734a74e

View on Chainz ↗

Height

#82,515

Difficulty

9.273953

Transactions

Size

203 B

Version

Bits

094621c9

Nonce

15,555

Timestamp

7/25/2013, 11:48:07 AM

Confirmations

6,712,869

Mined by

⛏️ P2SHAHGi8wDB5Q1pnktV2RKKJj33qeeKomrPdd

Merkle Root

2fe404bbedf460bbfd5b428e7e67d0aaf467be61721b52a205befe146bc11475

Transactions (1)

Coinbase2fe404bbedf460…befe146bc11475

1 in → 1 out11.6100 XPM109 B

AHGi8wDB…eKomrPdd

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.

3.024 × 10¹⁰⁵(106-digit number)

30249950784512556353…89295570696398985439

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

3.024 × 10¹⁰⁵(106-digit number)

30249950784512556353…89295570696398985439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.024 × 10¹⁰⁵(106-digit number)

30249950784512556353…89295570696398985441

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

6.049 × 10¹⁰⁵(106-digit number)

60499901569025112706…78591141392797970879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.049 × 10¹⁰⁵(106-digit number)

60499901569025112706…78591141392797970881

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

1.209 × 10¹⁰⁶(107-digit number)

12099980313805022541…57182282785595941759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.209 × 10¹⁰⁶(107-digit number)

12099980313805022541…57182282785595941761

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

2.419 × 10¹⁰⁶(107-digit number)

24199960627610045082…14364565571191883519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.419 × 10¹⁰⁶(107-digit number)

24199960627610045082…14364565571191883521

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

4.839 × 10¹⁰⁶(107-digit number)

48399921255220090165…28729131142383767039

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