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Block #411,709

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/20/2014, 12:17:41 AM Β· Difficulty 10.4210 Β· 6,389,624 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42653f349179610796de1cde936d390b3e21c394af2b881fd1d978de6eb9e403
View on Chainz β†—

Height

#411,709

Difficulty

10.420982

Transactions

2

Size

834 B

Version

2

Bits

0a6bc582

Nonce

1,060,179

Timestamp

2/20/2014, 12:17:41 AM

Confirmations

6,389,624

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

67e70f94f074ff98c903949d6bdf21fc0f60db3b181b55b8d64f2bedd8c57f59
Transactions (2)
Coinbaseb9650935caf4f4…9bf7cd5b1f54a9
1 in β†’ 1 out9.2000 XPM110 B
AeKNrjNj…1NEq95Ta
1f3da3b9a31f72…6260e61bae7995
4 in β†’ 1 out314.9900 XPM634 B
AUD9sSWZ…RTy7zMXE
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.

6.135 Γ— 10⁹⁡(96-digit number)
61352818485369460791…83956906158322634239
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
6.135 Γ— 10⁹⁡(96-digit number)
61352818485369460791…83956906158322634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁢(97-digit number)
12270563697073892158…67913812316645268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁢(97-digit number)
24541127394147784316…35827624633290536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.908 Γ— 10⁹⁢(97-digit number)
49082254788295568633…71655249266581073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.816 Γ— 10⁹⁢(97-digit number)
98164509576591137266…43310498533162147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.963 Γ— 10⁹⁷(98-digit number)
19632901915318227453…86620997066324295679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.926 Γ— 10⁹⁷(98-digit number)
39265803830636454906…73241994132648591359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.853 Γ— 10⁹⁷(98-digit number)
78531607661272909813…46483988265297182719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.570 Γ— 10⁹⁸(99-digit number)
15706321532254581962…92967976530594365439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.141 Γ— 10⁹⁸(99-digit number)
31412643064509163925…85935953061188730879
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:57,654,733 XPMΒ·at block #6,801,332 Β· updates every 60s
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