Block #84,982

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/27/2013, 4:10:22 AM · Difficulty 9.2807 · 6,705,961 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

1f21010ced02f22dea414cac54da1db7fd540cfb93155e512794d03db659501a

View on Chainz ↗

Height

#84,982

Difficulty

9.280707

Transactions

Size

203 B

Version

Bits

0947dc71

Nonce

230,956

Timestamp

7/27/2013, 4:10:22 AM

Confirmations

6,705,961

Merkle Root

ff9abafdac67cd3191d9afe49ef5026902cf4480cc822b88981f2c5b4d79014c

Transactions (1)

Coinbaseff9abafdac67cd…1f2c5b4d79014c

1 in → 1 out11.5900 XPM109 B

AcuJraLT…Y66BS47Q

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.

3.949 × 10¹⁰³(104-digit number)

39498728164775813179…64947783595757265999

Discovered Prime Numbers

p_k = 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.

origin − 1

3.949 × 10¹⁰³(104-digit number)

39498728164775813179…64947783595757265999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.899 × 10¹⁰³(104-digit number)

78997456329551626358…29895567191514531999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.579 × 10¹⁰⁴(105-digit number)

15799491265910325271…59791134383029063999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.159 × 10¹⁰⁴(105-digit number)

31598982531820650543…19582268766058127999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.319 × 10¹⁰⁴(105-digit number)

63197965063641301087…39164537532116255999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.263 × 10¹⁰⁵(106-digit number)

12639593012728260217…78329075064232511999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.527 × 10¹⁰⁵(106-digit number)

25279186025456520434…56658150128465023999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.055 × 10¹⁰⁵(106-digit number)

50558372050913040869…13316300256930047999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.011 × 10¹⁰⁶(107-digit number)

10111674410182608173…26632600513860095999

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 Cunningham Chain of the First Kind. 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer