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Block #441,502

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/13/2014, 4:47:16 AM Β· Difficulty 10.3483 Β· 6,372,813 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4cdf916a3f39d305b1fc01e4247f6abc62371d9be3509d5daca3fcfd5ddd8aae
View on Chainz β†—

Height

#441,502

Difficulty

10.348274

Transactions

1

Size

201 B

Version

2

Bits

0a592884

Nonce

36,379

Timestamp

3/13/2014, 4:47:16 AM

Confirmations

6,372,813

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e9e30ace1e2cd833854375abe76469aceb582fbd89ee8cebbb4075d8fc60666d
Transactions (1)
Coinbasee9e30ace1e2cd8…4075d8fc60666d
1 in β†’ 1 out9.3200 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.

3.630 Γ— 10⁹⁷(98-digit number)
36307519574665376257…04792364240953944479
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.630 Γ— 10⁹⁷(98-digit number)
36307519574665376257…04792364240953944479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.261 Γ— 10⁹⁷(98-digit number)
72615039149330752515…09584728481907888959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁸(99-digit number)
14523007829866150503…19169456963815777919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.904 Γ— 10⁹⁸(99-digit number)
29046015659732301006…38338913927631555839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.809 Γ— 10⁹⁸(99-digit number)
58092031319464602012…76677827855263111679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁹(100-digit number)
11618406263892920402…53355655710526223359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.323 Γ— 10⁹⁹(100-digit number)
23236812527785840804…06711311421052446719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.647 Γ— 10⁹⁹(100-digit number)
46473625055571681609…13422622842104893439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.294 Γ— 10⁹⁹(100-digit number)
92947250111143363219…26845245684209786879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.858 Γ— 10¹⁰⁰(101-digit number)
18589450022228672643…53690491368419573759
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,758,583 XPMΒ·at block #6,814,314 Β· updates every 60s
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