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Block #2,690,265

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2018, 3:29:01 PM Β· Difficulty 11.6839 Β· 4,151,379 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aca5613374c32153ed7503cde76ad0efb648b22bc5ceb0746477a83733aa0c5b
View on Chainz β†—

Height

#2,690,265

Difficulty

11.683913

Transactions

2

Size

1.10 KB

Version

2

Bits

0baf14f2

Nonce

820,145,674

Timestamp

6/3/2018, 3:29:01 PM

Confirmations

4,151,379

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

158f7d101f7fb54b4d60e10425fd4a37b9957782ad885c411e573d73849cfb18
Transactions (2)
Coinbase6ca2736d07ce62…2fc4db41ea556c
1 in β†’ 1 out7.3200 XPM110 B
Adqah8zh…1WwoHJ9t
03c1e27bd580f9…f45ecc49546567
6 in β†’ 1 out9999.9900 XPM931 B
ASpzvhG1…Wis5Gdbq
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.

6.191 Γ— 10⁹⁡(96-digit number)
61912750227758454617…99910506934170024001
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
6.191 Γ— 10⁹⁡(96-digit number)
61912750227758454617…99910506934170024001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.238 Γ— 10⁹⁢(97-digit number)
12382550045551690923…99821013868340048001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.476 Γ— 10⁹⁢(97-digit number)
24765100091103381847…99642027736680096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.953 Γ— 10⁹⁢(97-digit number)
49530200182206763694…99284055473360192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.906 Γ— 10⁹⁢(97-digit number)
99060400364413527388…98568110946720384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.981 Γ— 10⁹⁷(98-digit number)
19812080072882705477…97136221893440768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.962 Γ— 10⁹⁷(98-digit number)
39624160145765410955…94272443786881536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.924 Γ— 10⁹⁷(98-digit number)
79248320291530821910…88544887573763072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.584 Γ— 10⁹⁸(99-digit number)
15849664058306164382…77089775147526144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.169 Γ— 10⁹⁸(99-digit number)
31699328116612328764…54179550295052288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.339 Γ— 10⁹⁸(99-digit number)
63398656233224657528…08359100590104576001
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:57,977,538 XPMΒ·at block #6,841,643 Β· updates every 60s
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