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Block #2,804,661

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/22/2018, 7:25:09 AM Β· Difficulty 11.6671 Β· 4,032,053 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0cf4c6fe6e4e44ded759a4b20e2d4fa312f2ed9d15635b38a7a0a9d52e67681b
View on Chainz β†—

Height

#2,804,661

Difficulty

11.667112

Transactions

2

Size

1.14 KB

Version

2

Bits

0baac7d6

Nonce

209,625,963

Timestamp

8/22/2018, 7:25:09 AM

Confirmations

4,032,053

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

9e1b78e051499ef07e1c9296677bc067521045d05066510698ae1cfe24960f72
Transactions (2)
Coinbase662fc7f7c5db28…acc1f46f0c255c
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
3fbc43b9962d04…28558c57b9e594
6 in β†’ 2 out193.0543 XPM965 B
AH9z3v2J…BPKAH84wAMacMFhM…iFNVuut4
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.

6.927 Γ— 10⁹⁴(95-digit number)
69278803034024069256…35879999062876942881
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
6.927 Γ— 10⁹⁴(95-digit number)
69278803034024069256…35879999062876942881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.385 Γ— 10⁹⁡(96-digit number)
13855760606804813851…71759998125753885761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.771 Γ— 10⁹⁡(96-digit number)
27711521213609627702…43519996251507771521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.542 Γ— 10⁹⁡(96-digit number)
55423042427219255405…87039992503015543041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.108 Γ— 10⁹⁢(97-digit number)
11084608485443851081…74079985006031086081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.216 Γ— 10⁹⁢(97-digit number)
22169216970887702162…48159970012062172161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.433 Γ— 10⁹⁢(97-digit number)
44338433941775404324…96319940024124344321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.867 Γ— 10⁹⁢(97-digit number)
88676867883550808648…92639880048248688641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.773 Γ— 10⁹⁷(98-digit number)
17735373576710161729…85279760096497377281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.547 Γ— 10⁹⁷(98-digit number)
35470747153420323459…70559520192994754561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.094 Γ— 10⁹⁷(98-digit number)
70941494306840646918…41119040385989509121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,937,993 XPMΒ·at block #6,836,713 Β· updates every 60s
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