Block #87,546

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 11:45:58 PM · Difficulty 9.2738 · 6,714,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f899aa6f588474b244c57ae641bd8561eebb6c6d7727aa67c6aa1ff70aa086c5

View on Chainz ↗

Height

#87,546

Difficulty

9.273764

Transactions

Size

206 B

Version

Bits

09461565

Nonce

573,273

Timestamp

7/28/2013, 11:45:58 PM

Confirmations

6,714,908

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

e9b5ac556626d1742f842cec9f76f42e110538d71eceb97be225ef6399dc508a

Transactions (1)

Coinbasee9b5ac556626d1…25ef6399dc508a

1 in → 1 out11.6100 XPM109 B

AdhmaJ1p…MhFRDjQ7

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.

2.327 × 10¹¹⁰(111-digit number)

23274710043747409793…24806489582038693919

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

2.327 × 10¹¹⁰(111-digit number)

23274710043747409793…24806489582038693919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.327 × 10¹¹⁰(111-digit number)

23274710043747409793…24806489582038693921

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

4.654 × 10¹¹⁰(111-digit number)

46549420087494819587…49612979164077387839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.654 × 10¹¹⁰(111-digit number)

46549420087494819587…49612979164077387841

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

9.309 × 10¹¹⁰(111-digit number)

93098840174989639175…99225958328154775679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.309 × 10¹¹⁰(111-digit number)

93098840174989639175…99225958328154775681

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

1.861 × 10¹¹¹(112-digit number)

18619768034997927835…98451916656309551359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.861 × 10¹¹¹(112-digit number)

18619768034997927835…98451916656309551361

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

3.723 × 10¹¹¹(112-digit number)

37239536069995855670…96903833312619102719

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