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Block #429,319

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/4/2014, 5:04:42 PM Β· Difficulty 10.3467 Β· 6,367,168 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
16faa45364a51af0dadc5db1e645c8d9b4a5ad9a5293f08cc3068a8039c514b2
View on Chainz β†—

Height

#429,319

Difficulty

10.346653

Transactions

1

Size

202 B

Version

2

Bits

0a58be44

Nonce

568,907

Timestamp

3/4/2014, 5:04:42 PM

Confirmations

6,367,168

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

845124d5f9e96285c84e66433d8704c7510813242d6f18a307337916baf07b48
Transactions (1)
Coinbase845124d5f9e962…337916baf07b48
1 in β†’ 1 out9.3300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.296 Γ— 10⁹⁹(100-digit number)
22968186426486665273…22747386425159159801
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
2.296 Γ— 10⁹⁹(100-digit number)
22968186426486665273…22747386425159159801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.593 Γ— 10⁹⁹(100-digit number)
45936372852973330547…45494772850318319601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.187 Γ— 10⁹⁹(100-digit number)
91872745705946661095…90989545700636639201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.837 Γ— 10¹⁰⁰(101-digit number)
18374549141189332219…81979091401273278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.674 Γ— 10¹⁰⁰(101-digit number)
36749098282378664438…63958182802546556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.349 Γ— 10¹⁰⁰(101-digit number)
73498196564757328876…27916365605093113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.469 Γ— 10¹⁰¹(102-digit number)
14699639312951465775…55832731210186227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.939 Γ— 10¹⁰¹(102-digit number)
29399278625902931550…11665462420372454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.879 Γ— 10¹⁰¹(102-digit number)
58798557251805863101…23330924840744908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.175 Γ— 10¹⁰²(103-digit number)
11759711450361172620…46661849681489817601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,615,894 XPMΒ·at block #6,796,486 Β· updates every 60s
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