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Block #2,618,425

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/17/2018, 7:20:29 PM Β· Difficulty 11.2395 Β· 4,213,022 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e205ccc9ac688928df6d7f10bdffd4b77d350027b6deea884c68c2ff02a007f
View on Chainz β†—

Height

#2,618,425

Difficulty

11.239466

Transactions

1

Size

199 B

Version

2

Bits

0b3d4da8

Nonce

938,915,032

Timestamp

4/17/2018, 7:20:29 PM

Confirmations

4,213,022

Mined by

⛏️ P2SHAXYwsYvbgQ5zGE1o1ZmfZKQRG3R1bB5dJT

Merkle Root

7e8d1ab567a847eb4aa95d436857d1246d6d13811232a62a2b36837e33831235
Transactions (1)
Coinbase7e8d1ab567a847…36837e33831235
1 in β†’ 1 out7.9000 XPM109 B
AXYwsYvb…R1bB5dJT
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.

6.610 Γ— 10⁹⁴(95-digit number)
66101411277185911301…67340376334579061761
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
6.610 Γ— 10⁹⁴(95-digit number)
66101411277185911301…67340376334579061761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.322 Γ— 10⁹⁡(96-digit number)
13220282255437182260…34680752669158123521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.644 Γ— 10⁹⁡(96-digit number)
26440564510874364520…69361505338316247041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.288 Γ— 10⁹⁡(96-digit number)
52881129021748729041…38723010676632494081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10576225804349745808…77446021353264988161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.115 Γ— 10⁹⁢(97-digit number)
21152451608699491616…54892042706529976321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.230 Γ— 10⁹⁢(97-digit number)
42304903217398983233…09784085413059952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.460 Γ— 10⁹⁢(97-digit number)
84609806434797966466…19568170826119905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.692 Γ— 10⁹⁷(98-digit number)
16921961286959593293…39136341652239810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.384 Γ— 10⁹⁷(98-digit number)
33843922573919186586…78272683304479621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.768 Γ— 10⁹⁷(98-digit number)
67687845147838373172…56545366608959242241
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:57,895,741 XPMΒ·at block #6,831,446 Β· updates every 60s
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