Block #99,344

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 3:49:55 PM · Difficulty 9.3827 · 6,708,788 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

021e878e2fb018d0a27600270b0dcd9dd3a70a74ebf72bb5f5a7e7cb89a7976c

View on Chainz ↗

Height

#99,344

Difficulty

9.382724

Transactions

Size

202 B

Version

Bits

0961fa3b

Nonce

340,164

Timestamp

8/5/2013, 3:49:55 PM

Confirmations

6,708,788

Mined by

⛏️ P2SHAL4on7MoehvKsN2qMpn6JMVQDzcZpCa12j

Merkle Root

a73f2e15373e14715e9d6eed592e121b3ffc199bcbadcc2eb0cc0227a278a7d3

Transactions (1)

Coinbasea73f2e15373e14…cc0227a278a7d3

1 in → 1 out11.3400 XPM109 B

AL4on7Mo…cZpCa12j

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.

1.385 × 10¹⁰¹(102-digit number)

13854146352848513649…61021852862070330509

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

1.385 × 10¹⁰¹(102-digit number)

13854146352848513649…61021852862070330509

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.385 × 10¹⁰¹(102-digit number)

13854146352848513649…61021852862070330511

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

2.770 × 10¹⁰¹(102-digit number)

27708292705697027299…22043705724140661019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.770 × 10¹⁰¹(102-digit number)

27708292705697027299…22043705724140661021

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

5.541 × 10¹⁰¹(102-digit number)

55416585411394054598…44087411448281322039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.541 × 10¹⁰¹(102-digit number)

55416585411394054598…44087411448281322041

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

1.108 × 10¹⁰²(103-digit number)

11083317082278810919…88174822896562644079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.108 × 10¹⁰²(103-digit number)

11083317082278810919…88174822896562644081

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

2.216 × 10¹⁰²(103-digit number)

22166634164557621839…76349645793125288159

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 #99,344

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