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Block #2,642,445

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 5:54:02 PM Β· Difficulty 11.6529 Β· 4,194,925 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8cf3b99c319bd79f37b4465616f5200e49b09c1b6bb25b20cd1acb8b9cfc027e
View on Chainz β†—

Height

#2,642,445

Difficulty

11.652854

Transactions

1

Size

200 B

Version

2

Bits

0ba72169

Nonce

422,626,006

Timestamp

5/1/2018, 5:54:02 PM

Confirmations

4,194,925

Mined by

⛏️ P2SHAdE6TeUXZ4bLA142TdUTuvMC9mevbHhZUB

Merkle Root

4c827dfe24ae20ad70308ba9dbc247e4cbe79ccce799de56d9adcfb91299220d
Transactions (1)
Coinbase4c827dfe24ae20…adcfb91299220d
1 in β†’ 1 out7.3500 XPM110 B
AdE6TeUX…evbHhZUB
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.

1.278 Γ— 10⁹⁡(96-digit number)
12789029523792814833…50641300596478446401
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
1.278 Γ— 10⁹⁡(96-digit number)
12789029523792814833…50641300596478446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.557 Γ— 10⁹⁡(96-digit number)
25578059047585629667…01282601192956892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.115 Γ— 10⁹⁡(96-digit number)
51156118095171259335…02565202385913785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.023 Γ— 10⁹⁢(97-digit number)
10231223619034251867…05130404771827571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.046 Γ— 10⁹⁢(97-digit number)
20462447238068503734…10260809543655142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.092 Γ— 10⁹⁢(97-digit number)
40924894476137007468…20521619087310284801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.184 Γ— 10⁹⁢(97-digit number)
81849788952274014936…41043238174620569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.636 Γ— 10⁹⁷(98-digit number)
16369957790454802987…82086476349241139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.273 Γ— 10⁹⁷(98-digit number)
32739915580909605974…64172952698482278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.547 Γ— 10⁹⁷(98-digit number)
65479831161819211948…28345905396964556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.309 Γ— 10⁹⁸(99-digit number)
13095966232363842389…56691810793929113601
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:57,943,283 XPMΒ·at block #6,837,369 Β· updates every 60s
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