Block #93,451

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 10:42:10 AM · Difficulty 9.1963 · 6,701,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

670335168c5f7729e6a6fb6f4964a87c824538941b9bf5013942b96124dca00d

View on Chainz ↗

Height

#93,451

Difficulty

9.196275

Transactions

Size

1.22 KB

Version

Bits

09323f0e

Nonce

1,075

Timestamp

8/2/2013, 10:42:10 AM

Confirmations

6,701,464

Mined by

⛏️ P2SHAPjKFAPJALRzemGMeCWZRBGovp2eXz2PJB

Merkle Root

3fe35c571757b0565c167b00a8b16f2058699b221874d563e2428fb384402787

Transactions (3)

Coinbase7522667ca5ecb8…bd613e48dcec01

1 in → 1 out11.8400 XPM109 B

APjKFAPJ…2eXz2PJB

8c8a932efcc428…0ad1a1d0084963

5 in → 2 out8.7417 XPM817 B

ASb76Syb…6BiyZoCn ATGR4iiw…QWfHu1tz

3c91a917c2ac65…a0324438b26e29

1 in → 2 out4.4911 XPM225 B

AHMo39GL…iVQT9Gn6 AexfgFYA…pEmUU8rD

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.

1.798 × 10¹¹⁴(115-digit number)

17985815740520995429…78069264778764052859

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

1.798 × 10¹¹⁴(115-digit number)

17985815740520995429…78069264778764052859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.798 × 10¹¹⁴(115-digit number)

17985815740520995429…78069264778764052861

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

3.597 × 10¹¹⁴(115-digit number)

35971631481041990859…56138529557528105719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.597 × 10¹¹⁴(115-digit number)

35971631481041990859…56138529557528105721

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

7.194 × 10¹¹⁴(115-digit number)

71943262962083981718…12277059115056211439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.194 × 10¹¹⁴(115-digit number)

71943262962083981718…12277059115056211441

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

1.438 × 10¹¹⁵(116-digit number)

14388652592416796343…24554118230112422879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.438 × 10¹¹⁵(116-digit number)

14388652592416796343…24554118230112422881

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

2.877 × 10¹¹⁵(116-digit number)

28777305184833592687…49108236460224845759

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