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Block #2,653,119

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2018, 3:26:48 AM Β· Difficulty 11.7406 Β· 4,180,418 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b6c3a7ea187825625e2e860ce86d6e296dce6ba316bd5e345dde23d4a72b1145
View on Chainz β†—

Height

#2,653,119

Difficulty

11.740600

Transactions

2

Size

869 B

Version

2

Bits

0bbd97ef

Nonce

122,266,858

Timestamp

5/8/2018, 3:26:48 AM

Confirmations

4,180,418

Mined by

⛏️ P2SHAaR6Q1zQhQ9CAhsMDuuddeLuZPF7sVmRRK

Merkle Root

2c87d41e26e873691a3cd25f7d41c5176e9053c7258b1d2b1d941b06a931ad3d
Transactions (2)
Coinbase8ae354c569912f…02d89992294457
1 in β†’ 1 out7.2500 XPM110 B
AaR6Q1zQ…F7sVmRRK
12445c5cc7a072…6a1694aceae4b3
4 in β†’ 2 out350.0120 XPM669 B
ALucctRs…khDP6anfAeFrYq7G…rtPqJSLb
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.

3.017 Γ— 10⁹⁴(95-digit number)
30172564932122288740…22408657070477259361
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
3.017 Γ— 10⁹⁴(95-digit number)
30172564932122288740…22408657070477259361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.034 Γ— 10⁹⁴(95-digit number)
60345129864244577480…44817314140954518721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.206 Γ— 10⁹⁡(96-digit number)
12069025972848915496…89634628281909037441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.413 Γ— 10⁹⁡(96-digit number)
24138051945697830992…79269256563818074881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.827 Γ— 10⁹⁡(96-digit number)
48276103891395661984…58538513127636149761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.655 Γ— 10⁹⁡(96-digit number)
96552207782791323969…17077026255272299521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.931 Γ— 10⁹⁢(97-digit number)
19310441556558264793…34154052510544599041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.862 Γ— 10⁹⁢(97-digit number)
38620883113116529587…68308105021089198081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.724 Γ— 10⁹⁢(97-digit number)
77241766226233059175…36616210042178396161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.544 Γ— 10⁹⁷(98-digit number)
15448353245246611835…73232420084356792321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.089 Γ— 10⁹⁷(98-digit number)
30896706490493223670…46464840168713584641
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:57,912,495 XPMΒ·at block #6,833,536 Β· updates every 60s
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