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Block #215,764

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/18/2013, 7:40:13 AM Β· Difficulty 9.9255 Β· 6,592,374 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
250f9e34d2d210fb2894ebd1d7c007eafc517bde2c2ec63b28100855455512c0
View on Chainz β†—

Height

#215,764

Difficulty

9.925478

Transactions

2

Size

426 B

Version

2

Bits

09ecec18

Nonce

103,233

Timestamp

10/18/2013, 7:40:13 AM

Confirmations

6,592,374

Mined by

⛏️ P2SHASnpZxnjkmzGU4imShpxaqo5WueN9A3cys

Merkle Root

49bdbfeda07d4438271cbea2c8c7e7b724d644fbd76faab00af51a82a7c498de
Transactions (2)
Coinbase00224a18586341…3064d0e3b557f8
1 in β†’ 1 out10.1500 XPM109 B
ASnpZxnj…eN9A3cys
9aa97e0ae8e459…1aa9ea816356f1
1 in β†’ 2 out9.9902 XPM226 B
AGdBCZJy…n1xaExn3Addcs943…97RFdqoL
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.

1.360 Γ— 10⁹⁢(97-digit number)
13606402880629343131…68309967946941829121
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
1.360 Γ— 10⁹⁢(97-digit number)
13606402880629343131…68309967946941829121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.721 Γ— 10⁹⁢(97-digit number)
27212805761258686262…36619935893883658241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.442 Γ— 10⁹⁢(97-digit number)
54425611522517372525…73239871787767316481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10885122304503474505…46479743575534632961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.177 Γ— 10⁹⁷(98-digit number)
21770244609006949010…92959487151069265921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.354 Γ— 10⁹⁷(98-digit number)
43540489218013898020…85918974302138531841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.708 Γ— 10⁹⁷(98-digit number)
87080978436027796040…71837948604277063681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.741 Γ— 10⁹⁸(99-digit number)
17416195687205559208…43675897208554127361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.483 Γ— 10⁹⁸(99-digit number)
34832391374411118416…87351794417108254721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,709,146 XPMΒ·at block #6,808,137 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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