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Block #216,900

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/19/2013, 12:10:37 AM Β· Difficulty 9.9277 Β· 6,579,707 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
21eed0c7a821b0efe230d072154ae09767403bf2d2faeeaddc3076100e8ff1de
View on Chainz β†—

Height

#216,900

Difficulty

9.927682

Transactions

1

Size

199 B

Version

2

Bits

09ed7c8f

Nonce

16,849

Timestamp

10/19/2013, 12:10:37 AM

Confirmations

6,579,707

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

ac4260adbaad11c5775b353fea9c178c8c7f7834692672d2980dac32efe83fa7
Transactions (1)
Coinbaseac4260adbaad11…0dac32efe83fa7
1 in β†’ 1 out10.1300 XPM109 B
AH8MuWec…2bVG62mK
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.

1.750 Γ— 10⁹⁡(96-digit number)
17509546927625470623…20318281021559029681
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
1.750 Γ— 10⁹⁡(96-digit number)
17509546927625470623…20318281021559029681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.501 Γ— 10⁹⁡(96-digit number)
35019093855250941247…40636562043118059361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.003 Γ— 10⁹⁡(96-digit number)
70038187710501882494…81273124086236118721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.400 Γ— 10⁹⁢(97-digit number)
14007637542100376498…62546248172472237441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.801 Γ— 10⁹⁢(97-digit number)
28015275084200752997…25092496344944474881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.603 Γ— 10⁹⁢(97-digit number)
56030550168401505995…50184992689888949761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.120 Γ— 10⁹⁷(98-digit number)
11206110033680301199…00369985379777899521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.241 Γ— 10⁹⁷(98-digit number)
22412220067360602398…00739970759555799041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.482 Γ— 10⁹⁷(98-digit number)
44824440134721204796…01479941519111598081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.964 Γ— 10⁹⁷(98-digit number)
89648880269442409593…02959883038223196161
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:57,616,859 XPMΒ·at block #6,796,606 Β· updates every 60s
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