Block #273,877

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/26/2013, 12:46:13 AM · Difficulty 9.9560 · 6,557,568 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2fef0408cf62b9ab1b6f6fda84b1a2988ccb8015ce879569d70043125699309

Height

#273,877

Difficulty

9.955953

Transactions

1

Size

1.15 KB

Version

2

Bits

09f4b952

Nonce

215,808

Timestamp

11/26/2013, 12:46:13 AM

Confirmations

6,557,568

Merkle Root

903e49d2060bfe17da4f504194b653674509f8ec081471f04b0c09ed06266322
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.

3.958 × 10⁹⁵(96-digit number)
39582810875185343321…90260238203246116959
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.

1
origin − 1
3.958 × 10⁹⁵(96-digit number)
39582810875185343321…90260238203246116959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.916 × 10⁹⁵(96-digit number)
79165621750370686642…80520476406492233919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.583 × 10⁹⁶(97-digit number)
15833124350074137328…61040952812984467839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.166 × 10⁹⁶(97-digit number)
31666248700148274656…22081905625968935679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.333 × 10⁹⁶(97-digit number)
63332497400296549313…44163811251937871359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.266 × 10⁹⁷(98-digit number)
12666499480059309862…88327622503875742719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.533 × 10⁹⁷(98-digit number)
25332998960118619725…76655245007751485439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.066 × 10⁹⁷(98-digit number)
50665997920237239451…53310490015502970879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.013 × 10⁹⁸(99-digit number)
10133199584047447890…06620980031005941759
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, …
Circulating Supply:57,895,724 XPM·at block #6,831,444 · updates every 60s
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