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Block #2,745,219

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/12/2018, 5:13:07 AM Β· Difficulty 11.6466 Β· 4,097,138 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1784f8f844aec6ac933a0e0467d0dbbf61b3de8bd237f751f923a34a714fdd57
View on Chainz β†—

Height

#2,745,219

Difficulty

11.646613

Transactions

2

Size

428 B

Version

2

Bits

0ba5886b

Nonce

3,470,199

Timestamp

7/12/2018, 5:13:07 AM

Confirmations

4,097,138

Mined by

⛏️ P2SHAGLjq64chfe8UhjCrmuRgRRCzgQ4jxSWRw

Merkle Root

8d41ee61a5c0ec56b4d30b928a10b391aa57c218e940fa73522d9f01b2411bc3
Transactions (2)
Coinbase8f027a5cf3e5c1…eb29e19ceb370c
1 in β†’ 1 out7.3700 XPM110 B
AGLjq64c…Q4jxSWRw
95a93622639d43…23919aed873b49
1 in β†’ 2 out3.5094 XPM227 B
AT31Y5NT…v6ttP4hjAN7b55gz…YroqkbjU
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.

1.448 Γ— 10⁹⁢(97-digit number)
14484099607669342470…84781067195310541759
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.448 Γ— 10⁹⁢(97-digit number)
14484099607669342470…84781067195310541759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.896 Γ— 10⁹⁢(97-digit number)
28968199215338684940…69562134390621083519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.793 Γ— 10⁹⁢(97-digit number)
57936398430677369880…39124268781242167039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.158 Γ— 10⁹⁷(98-digit number)
11587279686135473976…78248537562484334079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.317 Γ— 10⁹⁷(98-digit number)
23174559372270947952…56497075124968668159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.634 Γ— 10⁹⁷(98-digit number)
46349118744541895904…12994150249937336319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.269 Γ— 10⁹⁷(98-digit number)
92698237489083791808…25988300499874672639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.853 Γ— 10⁹⁸(99-digit number)
18539647497816758361…51976600999749345279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.707 Γ— 10⁹⁸(99-digit number)
37079294995633516723…03953201999498690559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.415 Γ— 10⁹⁸(99-digit number)
74158589991267033447…07906403998997381119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.483 Γ— 10⁹⁹(100-digit number)
14831717998253406689…15812807997994762239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,983,263 XPMΒ·at block #6,842,356 Β· updates every 60s
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