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Block #2,815,532

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2018, 4:24:29 PM Β· Difficulty 11.6836 Β· 4,024,318 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
41e50543acc853fe455b1ec8729e3d778116e58e3a343cdff6ddc40090f79c09
View on Chainz β†—

Height

#2,815,532

Difficulty

11.683592

Transactions

1

Size

200 B

Version

2

Bits

0baeffdc

Nonce

267,090,246

Timestamp

8/29/2018, 4:24:29 PM

Confirmations

4,024,318

Mined by

⛏️ P2SHAY2CCMKNfcYbvrW8s6SMhoEzca29SZptas

Merkle Root

275f590387fa755e965c1e74df8669efda83318e8f4fee26100cc11df2d1da45
Transactions (1)
Coinbase275f590387fa75…0cc11df2d1da45
1 in β†’ 1 out7.3100 XPM110 B
AY2CCMKN…29SZptas
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.

3.496 Γ— 10⁹⁡(96-digit number)
34969113492213392741…09494398592683716481
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
3.496 Γ— 10⁹⁡(96-digit number)
34969113492213392741…09494398592683716481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.993 Γ— 10⁹⁡(96-digit number)
69938226984426785482…18988797185367432961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.398 Γ— 10⁹⁢(97-digit number)
13987645396885357096…37977594370734865921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.797 Γ— 10⁹⁢(97-digit number)
27975290793770714193…75955188741469731841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.595 Γ— 10⁹⁢(97-digit number)
55950581587541428386…51910377482939463681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.119 Γ— 10⁹⁷(98-digit number)
11190116317508285677…03820754965878927361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.238 Γ— 10⁹⁷(98-digit number)
22380232635016571354…07641509931757854721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.476 Γ— 10⁹⁷(98-digit number)
44760465270033142709…15283019863515709441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.952 Γ— 10⁹⁷(98-digit number)
89520930540066285418…30566039727031418881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.790 Γ— 10⁹⁸(99-digit number)
17904186108013257083…61132079454062837761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.580 Γ— 10⁹⁸(99-digit number)
35808372216026514167…22264158908125675521
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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