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Block #2,648,546

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2018, 2:22:10 PM Β· Difficulty 11.7664 Β· 4,185,354 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3951466fe40a2bd60d116acf79f303e93ebe91bd595034de117fc2afc0a23e51
View on Chainz β†—

Height

#2,648,546

Difficulty

11.766425

Transactions

1

Size

200 B

Version

2

Bits

0bc43474

Nonce

1,980,528,805

Timestamp

5/4/2018, 2:22:10 PM

Confirmations

4,185,354

Mined by

⛏️ P2SHARqFTUygffX9iNi55pB2Avp8iyRVD6wbpW

Merkle Root

8a4781587d2ba50b512383fbbd43a1272562d9fbd613bb0c0d3b3f143bd53dc3
Transactions (1)
Coinbase8a4781587d2ba5…3b3f143bd53dc3
1 in β†’ 1 out7.2100 XPM110 B
ARqFTUyg…RVD6wbpW
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.

1.745 Γ— 10⁹⁴(95-digit number)
17458618953407250624…06869132056581900801
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
1.745 Γ— 10⁹⁴(95-digit number)
17458618953407250624…06869132056581900801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.491 Γ— 10⁹⁴(95-digit number)
34917237906814501249…13738264113163801601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.983 Γ— 10⁹⁴(95-digit number)
69834475813629002498…27476528226327603201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.396 Γ— 10⁹⁡(96-digit number)
13966895162725800499…54953056452655206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.793 Γ— 10⁹⁡(96-digit number)
27933790325451600999…09906112905310412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.586 Γ— 10⁹⁡(96-digit number)
55867580650903201998…19812225810620825601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.117 Γ— 10⁹⁢(97-digit number)
11173516130180640399…39624451621241651201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.234 Γ— 10⁹⁢(97-digit number)
22347032260361280799…79248903242483302401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.469 Γ— 10⁹⁢(97-digit number)
44694064520722561598…58497806484966604801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.938 Γ— 10⁹⁢(97-digit number)
89388129041445123197…16995612969933209601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.787 Γ— 10⁹⁷(98-digit number)
17877625808289024639…33991225939866419201
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:57,915,425 XPMΒ·at block #6,833,899 Β· updates every 60s
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