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Block #366,883

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/19/2014, 4:45:01 PM Β· Difficulty 10.4355 Β· 6,442,261 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a513473c17fdd7ac3c5acbfdd65665b3398bb6ad7a22fd9d37be35d03118f9a9
View on Chainz β†—

Height

#366,883

Difficulty

10.435465

Transactions

1

Size

210 B

Version

2

Bits

0a6f7a9c

Nonce

771,953

Timestamp

1/19/2014, 4:45:01 PM

Confirmations

6,442,261

Mined by

⛏️ P2SHAd6bt69SstZerhCFqTfZCFaUaRPfMPqrnD

Merkle Root

d3500c0ebe71638d97b83b485fc4dda2deb1cdb4689d3960e4244c6235962a3d
Transactions (1)
Coinbased3500c0ebe7163…244c6235962a3d
1 in β†’ 1 out9.1700 XPM118 B
Ad6bt69S…PfMPqrnD
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.

2.489 Γ— 10⁹⁹(100-digit number)
24893059142553242656…63346938019593617921
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
2.489 Γ— 10⁹⁹(100-digit number)
24893059142553242656…63346938019593617921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.978 Γ— 10⁹⁹(100-digit number)
49786118285106485313…26693876039187235841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.957 Γ— 10⁹⁹(100-digit number)
99572236570212970626…53387752078374471681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.991 Γ— 10¹⁰⁰(101-digit number)
19914447314042594125…06775504156748943361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.982 Γ— 10¹⁰⁰(101-digit number)
39828894628085188250…13551008313497886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.965 Γ— 10¹⁰⁰(101-digit number)
79657789256170376501…27102016626995773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.593 Γ— 10¹⁰¹(102-digit number)
15931557851234075300…54204033253991546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.186 Γ— 10¹⁰¹(102-digit number)
31863115702468150600…08408066507983093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.372 Γ— 10¹⁰¹(102-digit number)
63726231404936301201…16816133015966187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.274 Γ— 10¹⁰²(103-digit number)
12745246280987260240…33632266031932375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.549 Γ— 10¹⁰²(103-digit number)
25490492561974520480…67264532063864750081
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
Circulating Supply:57,717,214 XPMΒ·at block #6,809,143 Β· updates every 60s
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