Block #130,384

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/23/2013, 1:23:51 PM · Difficulty 9.7855 · 6,696,752 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75fca1113dd445c04196d771fd383f2232671d8711ff7ce908951bac7d4db3ba

View on Chainz ↗

Height

#130,384

Difficulty

9.785533

Transactions

Size

829 B

Version

Bits

09c918ae

Nonce

456

Timestamp

8/23/2013, 1:23:51 PM

Confirmations

6,696,752

Mined by

⛏️ P2SHAZ4i99yYLDo4RvDFAKQyqHLagKdEU2pm6R

Merkle Root

ae7f677f68cffce11b9b5298adc300e43f6fa2987e46a552ae2d5267081e7c96

Transactions (2)

Coinbased344eaea3faa15…f61553dcbd1c25

1 in → 1 out10.4400 XPM100 B

AZ4i99yY…dEU2pm6R

f57ba518c441ba…b55d7167513153

4 in → 2 out30.0183 XPM636 B

Ace2CeZc…jof6khc7 AMuJG9no…PKhLUKVP

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.

7.322 × 10¹⁰¹(102-digit number)

73227529830778187364…18646857513413079859

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

7.322 × 10¹⁰¹(102-digit number)

73227529830778187364…18646857513413079859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.322 × 10¹⁰¹(102-digit number)

73227529830778187364…18646857513413079861

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

1.464 × 10¹⁰²(103-digit number)

14645505966155637472…37293715026826159719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.464 × 10¹⁰²(103-digit number)

14645505966155637472…37293715026826159721

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

2.929 × 10¹⁰²(103-digit number)

29291011932311274945…74587430053652319439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.929 × 10¹⁰²(103-digit number)

29291011932311274945…74587430053652319441

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

5.858 × 10¹⁰²(103-digit number)

58582023864622549891…49174860107304638879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.858 × 10¹⁰²(103-digit number)

58582023864622549891…49174860107304638881

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

1.171 × 10¹⁰³(104-digit number)

11716404772924509978…98349720214609277759

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 #130,384

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