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Block #2,184,814

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/29/2017, 2:36:28 PM Β· Difficulty 10.9437 Β· 4,655,793 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d27d1bacd51d4e52e48aff0d71a22aba1bf69eb9ffbde5162dd44b978198c61c
View on Chainz β†—

Height

#2,184,814

Difficulty

10.943664

Transactions

2

Size

424 B

Version

2

Bits

0af193f0

Nonce

186,415,754

Timestamp

6/29/2017, 2:36:28 PM

Confirmations

4,655,793

Mined by

⛏️ P2SHAPpzzTiz319NdBJQusBBYLX3M8ESxi3u6Q

Merkle Root

1dd00c76b7ff9a8466b1a2faacde88906c1b0ed05ecd5f794b387d80874d0a71
Transactions (2)
Coinbase2bd6c9deee1689…8747eb2d7feb4c
1 in β†’ 1 out8.3500 XPM109 B
APpzzTiz…ESxi3u6Q
cdd84d56260521…a916e9dd312a6a
1 in β†’ 2 out3536.4819 XPM226 B
AMNqyy2W…ise9w8w1AS4do598…Btn6CUiR
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.

2.163 Γ— 10⁹³(94-digit number)
21633277660559051830…78719962404411163521
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
2.163 Γ— 10⁹³(94-digit number)
21633277660559051830…78719962404411163521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.326 Γ— 10⁹³(94-digit number)
43266555321118103660…57439924808822327041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.653 Γ— 10⁹³(94-digit number)
86533110642236207320…14879849617644654081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.730 Γ— 10⁹⁴(95-digit number)
17306622128447241464…29759699235289308161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.461 Γ— 10⁹⁴(95-digit number)
34613244256894482928…59519398470578616321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.922 Γ— 10⁹⁴(95-digit number)
69226488513788965856…19038796941157232641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.384 Γ— 10⁹⁡(96-digit number)
13845297702757793171…38077593882314465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.769 Γ— 10⁹⁡(96-digit number)
27690595405515586342…76155187764628930561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.538 Γ— 10⁹⁡(96-digit number)
55381190811031172685…52310375529257861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.107 Γ— 10⁹⁢(97-digit number)
11076238162206234537…04620751058515722241
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:57,969,192 XPMΒ·at block #6,840,606 Β· updates every 60s
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