Block #81,811

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 12:29:54 AM · Difficulty 9.2703 · 6,725,986 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ccba0e404f4813c186511f0ccab51b05daee576cbe5bdf49768dd00228886252

View on Chainz ↗

Height

#81,811

Difficulty

9.270280

Transactions

Size

370 B

Version

Bits

0945311a

Nonce

10,393

Timestamp

7/25/2013, 12:29:54 AM

Confirmations

6,725,986

Mined by

⛏️ P2SHAMRJBb3V94CDPb3SssTj1B2eiHZv15uY6D

Merkle Root

7686670cf704aff3ab4a221b8a9e0faa107bae0b426fdc2a68c031496046e76c

Transactions (2)

Coinbase2a9fad2115497e…3787c1def56c94

1 in → 1 out11.6300 XPM109 B

AMRJBb3V…Zv15uY6D

d834ea0d87f835…b52a6c3e02d6ae

1 in → 1 out11.7300 XPM158 B

AaNMrVuB…vz8xMmHF

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.

2.431 × 10¹²⁵(126-digit number)

24312802403694525667…21760404432299101799

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

2.431 × 10¹²⁵(126-digit number)

24312802403694525667…21760404432299101799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.431 × 10¹²⁵(126-digit number)

24312802403694525667…21760404432299101801

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

4.862 × 10¹²⁵(126-digit number)

48625604807389051335…43520808864598203599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.862 × 10¹²⁵(126-digit number)

48625604807389051335…43520808864598203601

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

9.725 × 10¹²⁵(126-digit number)

97251209614778102671…87041617729196407199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.725 × 10¹²⁵(126-digit number)

97251209614778102671…87041617729196407201

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

1.945 × 10¹²⁶(127-digit number)

19450241922955620534…74083235458392814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.945 × 10¹²⁶(127-digit number)

19450241922955620534…74083235458392814401

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

3.890 × 10¹²⁶(127-digit number)

38900483845911241068…48166470916785628799

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 #81,811

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