Block #85,942

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 6:50:35 PM · Difficulty 9.2919 · 6,723,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e73240ba5f8b5b350bec2a0fad2b6cf7601287deed26b8ac69f540b5257cf55

View on Chainz ↗

Height

#85,942

Difficulty

9.291851

Transactions

Size

204 B

Version

Bits

094ab6bb

Nonce

30,210

Timestamp

7/27/2013, 6:50:35 PM

Confirmations

6,723,648

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

41e34b8eb4a1e0415658c01cc566b7ee4b499b7ebb585cf385dc4ef2ebbeaa80

Transactions (1)

Coinbase41e34b8eb4a1e0…dc4ef2ebbeaa80

1 in → 1 out11.5700 XPM109 B

AcBadmkp…GmhL921o

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.

2.050 × 10¹⁰⁷(108-digit number)

20508219446122880447…66389988028671217099

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

2.050 × 10¹⁰⁷(108-digit number)

20508219446122880447…66389988028671217099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.050 × 10¹⁰⁷(108-digit number)

20508219446122880447…66389988028671217101

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

4.101 × 10¹⁰⁷(108-digit number)

41016438892245760895…32779976057342434199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.101 × 10¹⁰⁷(108-digit number)

41016438892245760895…32779976057342434201

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

8.203 × 10¹⁰⁷(108-digit number)

82032877784491521791…65559952114684868399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.203 × 10¹⁰⁷(108-digit number)

82032877784491521791…65559952114684868401

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

1.640 × 10¹⁰⁸(109-digit number)

16406575556898304358…31119904229369736799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.640 × 10¹⁰⁸(109-digit number)

16406575556898304358…31119904229369736801

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

3.281 × 10¹⁰⁸(109-digit number)

32813151113796608716…62239808458739473599

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 #85,942

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