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Block #491,205

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/14/2014, 8:56:50 AM Β· Difficulty 10.6804 Β· 6,312,259 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
219243cec553a5e17d2a81adb2a7d1bd0e59a88385762900bd86275ba6da6c8a
View on Chainz β†—

Height

#491,205

Difficulty

10.680408

Transactions

1

Size

200 B

Version

2

Bits

0aae2f39

Nonce

357,716

Timestamp

4/14/2014, 8:56:50 AM

Confirmations

6,312,259

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

cb532e02b3dbf79189aae599cdff96c887fb5baf5d8c0bf534e70efdd1668d30
Transactions (1)
Coinbasecb532e02b3dbf7…e70efdd1668d30
1 in β†’ 1 out8.7500 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.

1.602 Γ— 10⁹⁡(96-digit number)
16025637005900359024…71358116691598944001
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
1.602 Γ— 10⁹⁡(96-digit number)
16025637005900359024…71358116691598944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.205 Γ— 10⁹⁡(96-digit number)
32051274011800718048…42716233383197888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.410 Γ— 10⁹⁡(96-digit number)
64102548023601436096…85432466766395776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.282 Γ— 10⁹⁢(97-digit number)
12820509604720287219…70864933532791552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.564 Γ— 10⁹⁢(97-digit number)
25641019209440574438…41729867065583104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.128 Γ— 10⁹⁢(97-digit number)
51282038418881148876…83459734131166208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.025 Γ— 10⁹⁷(98-digit number)
10256407683776229775…66919468262332416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.051 Γ— 10⁹⁷(98-digit number)
20512815367552459550…33838936524664832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.102 Γ— 10⁹⁷(98-digit number)
41025630735104919101…67677873049329664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.205 Γ— 10⁹⁷(98-digit number)
82051261470209838202…35355746098659328001
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:57,671,740 XPMΒ·at block #6,803,463 Β· updates every 60s
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