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Block #216,399

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/18/2013, 5:17:36 PM Β· Difficulty 9.9264 Β· 6,626,993 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b16ec49cbbd48e3caa3727fbe2842d664b90823ccd880cc85e724ce3e78578dd
View on Chainz β†—

Height

#216,399

Difficulty

9.926385

Transactions

1

Size

207 B

Version

2

Bits

09ed278b

Nonce

1,235

Timestamp

10/18/2013, 5:17:36 PM

Confirmations

6,626,993

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

a554cf9a212540375c7b44578bf51e0949bb544963c0bd0f72beea20a02273c9
Transactions (1)
Coinbasea554cf9a212540…beea20a02273c9
1 in β†’ 1 out10.1300 XPM116 B
AcLBm5Z9…S683d7c3
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.

9.540 Γ— 10⁹⁡(96-digit number)
95405155453574856448…63911235264558237881
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
9.540 Γ— 10⁹⁡(96-digit number)
95405155453574856448…63911235264558237881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.908 Γ— 10⁹⁢(97-digit number)
19081031090714971289…27822470529116475761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.816 Γ— 10⁹⁢(97-digit number)
38162062181429942579…55644941058232951521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.632 Γ— 10⁹⁢(97-digit number)
76324124362859885158…11289882116465903041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.526 Γ— 10⁹⁷(98-digit number)
15264824872571977031…22579764232931806081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.052 Γ— 10⁹⁷(98-digit number)
30529649745143954063…45159528465863612161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.105 Γ— 10⁹⁷(98-digit number)
61059299490287908126…90319056931727224321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.221 Γ— 10⁹⁸(99-digit number)
12211859898057581625…80638113863454448641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.442 Γ— 10⁹⁸(99-digit number)
24423719796115163250…61276227726908897281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.884 Γ— 10⁹⁸(99-digit number)
48847439592230326501…22552455453817794561
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
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