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Block #2,639,023

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 12:16:49 PM Β· Difficulty 11.5188 Β· 4,198,624 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
689dc35d97c0583322188175fbd6223a1cf1f044fe216414810f3e02086f18b0
View on Chainz β†—

Height

#2,639,023

Difficulty

11.518824

Transactions

1

Size

201 B

Version

2

Bits

0b84d1a9

Nonce

64,196,201

Timestamp

4/30/2018, 12:16:49 PM

Confirmations

4,198,624

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

cf6d2332058c56f4b426ab730d0d8beb7a03ad449ea97f58b899d036db15879b
Transactions (1)
Coinbasecf6d2332058c56…99d036db15879b
1 in β†’ 1 out7.5200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.918 Γ— 10⁹⁢(97-digit number)
29181704514267122047…54993215728055877121
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
2.918 Γ— 10⁹⁢(97-digit number)
29181704514267122047…54993215728055877121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.836 Γ— 10⁹⁢(97-digit number)
58363409028534244095…09986431456111754241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.167 Γ— 10⁹⁷(98-digit number)
11672681805706848819…19972862912223508481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.334 Γ— 10⁹⁷(98-digit number)
23345363611413697638…39945725824447016961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.669 Γ— 10⁹⁷(98-digit number)
46690727222827395276…79891451648894033921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.338 Γ— 10⁹⁷(98-digit number)
93381454445654790552…59782903297788067841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.867 Γ— 10⁹⁸(99-digit number)
18676290889130958110…19565806595576135681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.735 Γ— 10⁹⁸(99-digit number)
37352581778261916221…39131613191152271361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.470 Γ— 10⁹⁸(99-digit number)
74705163556523832442…78263226382304542721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.494 Γ— 10⁹⁹(100-digit number)
14941032711304766488…56526452764609085441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.988 Γ— 10⁹⁹(100-digit number)
29882065422609532976…13052905529218170881
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:57,945,503 XPMΒ·at block #6,837,646 Β· updates every 60s
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