Block #74,533

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 11:38:05 AM · Difficulty 8.9956 · 6,738,156 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

809807c22d6625667d33b0ee94f634a535ea7c426535d240a9f9ec1112a1a234

View on Chainz ↗

Height

#74,533

Difficulty

8.995567

Transactions

Size

1.80 KB

Version

Bits

08fedd78

Nonce

443

Timestamp

7/21/2013, 11:38:05 AM

Confirmations

6,738,156

Mined by

⛏️ P2SHAUyCUQiNFZhVxeC6sXYgBoFyADQT6tQfrn

Merkle Root

1af3db241fd7264174a813b77c353b59094e328ce114e615e79a452a8b0fd617

Transactions (3)

Coinbase945c8652539f43…dff3e8a146be20

1 in → 1 out12.3700 XPM110 B

AUyCUQiN…QT6tQfrn

eb9a034b020f82…6c23c90a3b4666

2 in → 1 out24.6900 XPM271 B

AcjRZamd…XfNvPJsT

c5fbea3efe118f…5125f7bb903cfb

9 in → 1 out110.7000 XPM1.34 KB

AT7qMwzf…wikE2aVB

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.

2.657 × 10¹⁰⁶(107-digit number)

26575027453958123012…08597991929327627499

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

2.657 × 10¹⁰⁶(107-digit number)

26575027453958123012…08597991929327627499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.657 × 10¹⁰⁶(107-digit number)

26575027453958123012…08597991929327627501

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

5.315 × 10¹⁰⁶(107-digit number)

53150054907916246024…17195983858655254999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.315 × 10¹⁰⁶(107-digit number)

53150054907916246024…17195983858655255001

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

1.063 × 10¹⁰⁷(108-digit number)

10630010981583249204…34391967717310509999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.063 × 10¹⁰⁷(108-digit number)

10630010981583249204…34391967717310510001

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

2.126 × 10¹⁰⁷(108-digit number)

21260021963166498409…68783935434621019999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.126 × 10¹⁰⁷(108-digit number)

21260021963166498409…68783935434621020001

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

4.252 × 10¹⁰⁷(108-digit number)

42520043926332996819…37567870869242039999

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 #74,533

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