Block #85,554

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 12:30:16 PM · Difficulty 9.2908 · 6,707,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbad2af8bdaab5813441cfb793f6787b19fbedf526e9bc1bc35d1b078a2529e4

View on Chainz ↗

Height

#85,554

Difficulty

9.290840

Transactions

Size

1.25 KB

Version

Bits

094a747e

Nonce

10,375

Timestamp

7/27/2013, 12:30:16 PM

Confirmations

6,707,186

Merkle Root

c2a4695112f6a5852efb6a1c01563800d2c8da13e8cb93caebc44e589654d6b7

Transactions (3)

Coinbase6026ad1247c9df…3851cd590bd2e6

1 in → 1 out11.5900 XPM109 B

AWmMb6bf…eGJUrYi4

4bcf121fc09cfe…fe8b559a0f542c

5 in → 2 out1.7530 XPM816 B

AagV1rYx…13ESXeTK ASM8Jkca…bYJT391f

aa1af63c1cd6cd…28c20d735fff7b

1 in → 3 out7.7600 XPM261 B

AUxC2GFy…qGAXVVUe AcWVSMpG…Smxw36B8 AP9mfqWR…bTKzmopG

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.

2.611 × 10¹⁰⁵(106-digit number)

26112405176826216355…24306736782372147959

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

2.611 × 10¹⁰⁵(106-digit number)

26112405176826216355…24306736782372147959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.611 × 10¹⁰⁵(106-digit number)

26112405176826216355…24306736782372147961

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

5.222 × 10¹⁰⁵(106-digit number)

52224810353652432710…48613473564744295919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.222 × 10¹⁰⁵(106-digit number)

52224810353652432710…48613473564744295921

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

1.044 × 10¹⁰⁶(107-digit number)

10444962070730486542…97226947129488591839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.044 × 10¹⁰⁶(107-digit number)

10444962070730486542…97226947129488591841

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

2.088 × 10¹⁰⁶(107-digit number)

20889924141460973084…94453894258977183679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.088 × 10¹⁰⁶(107-digit number)

20889924141460973084…94453894258977183681

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

4.177 × 10¹⁰⁶(107-digit number)

41779848282921946168…88907788517954367359

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