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Block #434,856

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/8/2014, 12:59:44 PM Β· Difficulty 10.3525 Β· 6,408,062 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ffe362bf0a655b95bbc51679da38a844126b6c116ef78a4524cc90332d11cf2
View on Chainz β†—

Height

#434,856

Difficulty

10.352513

Transactions

1

Size

189 B

Version

2

Bits

0a5a3e53

Nonce

93,360

Timestamp

3/8/2014, 12:59:44 PM

Confirmations

6,408,062

Mined by

⛏️ aSANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

d7a4a68d1efe4cf69012886d041ee7a7c11fd3ca2f9b3a87ea1e19f8a4bc4719
Transactions (1)
Coinbased7a4a68d1efe4c…1e19f8a4bc4719
1 in β†’ 1 out9.3200 XPM97 B
ANEZwy9t…E1uf5dKY
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.

1.831 Γ— 10¹⁰⁰(101-digit number)
18318812343473015001…62494160183550198401
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
1.831 Γ— 10¹⁰⁰(101-digit number)
18318812343473015001…62494160183550198401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.663 Γ— 10¹⁰⁰(101-digit number)
36637624686946030002…24988320367100396801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.327 Γ— 10¹⁰⁰(101-digit number)
73275249373892060004…49976640734200793601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.465 Γ— 10¹⁰¹(102-digit number)
14655049874778412000…99953281468401587201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.931 Γ— 10¹⁰¹(102-digit number)
29310099749556824001…99906562936803174401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.862 Γ— 10¹⁰¹(102-digit number)
58620199499113648003…99813125873606348801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.172 Γ— 10¹⁰²(103-digit number)
11724039899822729600…99626251747212697601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.344 Γ— 10¹⁰²(103-digit number)
23448079799645459201…99252503494425395201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.689 Γ— 10¹⁰²(103-digit number)
46896159599290918403…98505006988850790401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.379 Γ— 10¹⁰²(103-digit number)
93792319198581836806…97010013977701580801
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:57,987,691 XPMΒ·at block #6,842,917 Β· updates every 60s
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