Block #373,694

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 12:21:07 PM · Difficulty 10.4246 · 6,436,202 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6df87ea45778297f45f0eb74a0f906e061dae0330998b18e5d4b0b1967cd7be1

Height

#373,694

Difficulty

10.424622

Transactions

4

Size

1.60 KB

Version

2

Bits

0a6cb402

Nonce

797,182

Timestamp

1/24/2014, 12:21:07 PM

Confirmations

6,436,202

Merkle Root

7279407fb1821e12de1eb877fc389988e3401547c47e1ced1bed739e84551e02
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.

3.247 × 10⁹⁹(100-digit number)
32475706934432536525…01803698749159323201
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
3.247 × 10⁹⁹(100-digit number)
32475706934432536525…01803698749159323201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.495 × 10⁹⁹(100-digit number)
64951413868865073051…03607397498318646401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.299 × 10¹⁰⁰(101-digit number)
12990282773773014610…07214794996637292801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.598 × 10¹⁰⁰(101-digit number)
25980565547546029220…14429589993274585601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.196 × 10¹⁰⁰(101-digit number)
51961131095092058441…28859179986549171201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.039 × 10¹⁰¹(102-digit number)
10392226219018411688…57718359973098342401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.078 × 10¹⁰¹(102-digit number)
20784452438036823376…15436719946196684801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.156 × 10¹⁰¹(102-digit number)
41568904876073646752…30873439892393369601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.313 × 10¹⁰¹(102-digit number)
83137809752147293505…61746879784786739201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.662 × 10¹⁰²(103-digit number)
16627561950429458701…23493759569573478401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.325 × 10¹⁰²(103-digit number)
33255123900858917402…46987519139146956801
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,723,249 XPM·at block #6,809,895 · updates every 60s
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