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Block #2,648,200

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2018, 8:57:34 AM Β· Difficulty 11.7654 Β· 4,157,633 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
33b326c4a689eafe4c26e01fb5cc272a27275a53d1624be8af9d6400c47935b9
View on Chainz β†—

Height

#2,648,200

Difficulty

11.765439

Transactions

2

Size

575 B

Version

2

Bits

0bc3f3d3

Nonce

363,954,797

Timestamp

5/4/2018, 8:57:34 AM

Confirmations

4,157,633

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

6b80d5f28e7d77172491b86d8f0131b6cd5e80a00fd6bde17f384d8dd0b03444
Transactions (2)
Coinbaseead4c2166b57dc…2b2ec71450679d
1 in β†’ 1 out7.2200 XPM110 B
Adqah8zh…1WwoHJ9t
c882bff72cc15a…c43e53da994d10
2 in β†’ 2 out0.3966 XPM374 B
AThaWe4S…HmpAG8VoAM2AK8zu…mMMVm4jy
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.

6.456 Γ— 10⁹⁢(97-digit number)
64568440629378869533…23522650395672565761
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
6.456 Γ— 10⁹⁢(97-digit number)
64568440629378869533…23522650395672565761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.291 Γ— 10⁹⁷(98-digit number)
12913688125875773906…47045300791345131521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.582 Γ— 10⁹⁷(98-digit number)
25827376251751547813…94090601582690263041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.165 Γ— 10⁹⁷(98-digit number)
51654752503503095626…88181203165380526081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.033 Γ— 10⁹⁸(99-digit number)
10330950500700619125…76362406330761052161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.066 Γ— 10⁹⁸(99-digit number)
20661901001401238250…52724812661522104321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.132 Γ— 10⁹⁸(99-digit number)
41323802002802476501…05449625323044208641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.264 Γ— 10⁹⁸(99-digit number)
82647604005604953002…10899250646088417281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.652 Γ— 10⁹⁹(100-digit number)
16529520801120990600…21798501292176834561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.305 Γ— 10⁹⁹(100-digit number)
33059041602241981200…43597002584353669121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.611 Γ— 10⁹⁹(100-digit number)
66118083204483962401…87194005168707338241
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:57,690,751 XPMΒ·at block #6,805,832 Β· updates every 60s
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