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Block #2,685,583

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/31/2018, 8:28:52 AM Β· Difficulty 11.6874 Β· 4,156,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
176a7a2d58a53a4c4a58b0bf31513a2d2ff326140fe555759fe446c38defb160
View on Chainz β†—

Height

#2,685,583

Difficulty

11.687376

Transactions

1

Size

200 B

Version

2

Bits

0baff7e8

Nonce

1,006,089,339

Timestamp

5/31/2018, 8:28:52 AM

Confirmations

4,156,445

Mined by

⛏️ P2SHAH49fwfncENxqwwMt5XSsgnmA3bUkxJ8yg

Merkle Root

4da6077da81da7e232c50780ad3c29197c238aab4bf04c9cee5aa3de3005a315
Transactions (1)
Coinbase4da6077da81da7…5aa3de3005a315
1 in β†’ 1 out7.3100 XPM110 B
AH49fwfn…bUkxJ8yg
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.291 Γ— 10⁹⁡(96-digit number)
32919367952423311753…96131078398244224001
Discovered Prime Numbers
p_k = 2^k Γ— 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
3.291 Γ— 10⁹⁡(96-digit number)
32919367952423311753…96131078398244224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.583 Γ— 10⁹⁡(96-digit number)
65838735904846623507…92262156796488448001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.316 Γ— 10⁹⁢(97-digit number)
13167747180969324701…84524313592976896001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.633 Γ— 10⁹⁢(97-digit number)
26335494361938649402…69048627185953792001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.267 Γ— 10⁹⁢(97-digit number)
52670988723877298805…38097254371907584001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.053 Γ— 10⁹⁷(98-digit number)
10534197744775459761…76194508743815168001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.106 Γ— 10⁹⁷(98-digit number)
21068395489550919522…52389017487630336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.213 Γ— 10⁹⁷(98-digit number)
42136790979101839044…04778034975260672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.427 Γ— 10⁹⁷(98-digit number)
84273581958203678089…09556069950521344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.685 Γ— 10⁹⁸(99-digit number)
16854716391640735617…19112139901042688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.370 Γ— 10⁹⁸(99-digit number)
33709432783281471235…38224279802085376001
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
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