Block #85,638

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 1:49:22 PM · Difficulty 9.2915 · 6,725,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0d91cdf958c5f5d157948ba6d89e0f2b003ce88a2b32e3c4ebd0a35bf63b370

View on Chainz ↗

Height

#85,638

Difficulty

9.291519

Transactions

Size

206 B

Version

Bits

094aa0ff

Nonce

125,714

Timestamp

7/27/2013, 1:49:22 PM

Confirmations

6,725,063

Mined by

⛏️ P2SHALwPmuqr3b2kNHPdD7pqRMfLqh6vuSDJsv

Merkle Root

f1cf9b9fa211267d21e338a84d052512576039c477f616d384f6e76e17bb4a8f

Transactions (1)

Coinbasef1cf9b9fa21126…f6e76e17bb4a8f

1 in → 1 out11.5700 XPM109 B

ALwPmuqr…6vuSDJsv

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.

1.125 × 10¹¹¹(112-digit number)

11252674694975586134…20760294442198074279

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

1.125 × 10¹¹¹(112-digit number)

11252674694975586134…20760294442198074279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.125 × 10¹¹¹(112-digit number)

11252674694975586134…20760294442198074281

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

2.250 × 10¹¹¹(112-digit number)

22505349389951172268…41520588884396148559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.250 × 10¹¹¹(112-digit number)

22505349389951172268…41520588884396148561

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

4.501 × 10¹¹¹(112-digit number)

45010698779902344536…83041177768792297119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.501 × 10¹¹¹(112-digit number)

45010698779902344536…83041177768792297121

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

9.002 × 10¹¹¹(112-digit number)

90021397559804689073…66082355537584594239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.002 × 10¹¹¹(112-digit number)

90021397559804689073…66082355537584594241

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

1.800 × 10¹¹²(113-digit number)

18004279511960937814…32164711075169188479

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 #85,638

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