Block #93,450

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 10:41:46 AM · Difficulty 9.1962 · 6,701,601 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f021ad6c1b61e04d4b03ed7cde6884566a386d9d408d0962e367c6377506c8b3

View on Chainz ↗

Height

#93,450

Difficulty

9.196219

Transactions

Size

432 B

Version

Bits

09323b65

Nonce

43,117

Timestamp

8/2/2013, 10:41:46 AM

Confirmations

6,701,601

Mined by

⛏️ P2SHAKcsvMv6r6V5iZTkF5PjxbScdK4AGCie98

Merkle Root

5c8444de5acda50d7e12b75af78fcc323de722ab69d930c690949a4acbf7b5e9

Transactions (2)

Coinbase0493ee48919d93…6486fe35047323

1 in → 1 out11.8200 XPM109 B

AKcsvMv6…4AGCie98

46e1490182aacc…6538c47ed719d0

1 in → 2 out6.5011 XPM226 B

ASb76Syb…6BiyZoCn AQCGZ3ww…SyzCPJw3

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.

2.524 × 10¹¹⁰(111-digit number)

25249151317742457008…94992068465194745739

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

2.524 × 10¹¹⁰(111-digit number)

25249151317742457008…94992068465194745739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.524 × 10¹¹⁰(111-digit number)

25249151317742457008…94992068465194745741

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

5.049 × 10¹¹⁰(111-digit number)

50498302635484914017…89984136930389491479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.049 × 10¹¹⁰(111-digit number)

50498302635484914017…89984136930389491481

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

1.009 × 10¹¹¹(112-digit number)

10099660527096982803…79968273860778982959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.009 × 10¹¹¹(112-digit number)

10099660527096982803…79968273860778982961

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

2.019 × 10¹¹¹(112-digit number)

20199321054193965607…59936547721557965919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.019 × 10¹¹¹(112-digit number)

20199321054193965607…59936547721557965921

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

4.039 × 10¹¹¹(112-digit number)

40398642108387931214…19873095443115931839

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