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Block #2,658,531

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/12/2018, 10:18:03 PM Β· Difficulty 11.6524 Β· 4,184,865 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7180ef983fe53bae216e9e47714ab1560f9f877683fc20fe7408bd8190b35445
View on Chainz β†—

Height

#2,658,531

Difficulty

11.652447

Transactions

1

Size

201 B

Version

2

Bits

0ba706bd

Nonce

1,988,538,784

Timestamp

5/12/2018, 10:18:03 PM

Confirmations

4,184,865

Mined by

⛏️ P2SHAaNbprLfvd68WjKjkVtQUZCRfSPTE28mr7

Merkle Root

5f6ff83c5eb0b9bcff35eed5bf12a858c965e96f79e0a8774e89901da81b2247
Transactions (1)
Coinbase5f6ff83c5eb0b9…89901da81b2247
1 in β†’ 1 out7.3500 XPM110 B
AaNbprLf…PTE28mr7
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.

1.204 Γ— 10⁹⁷(98-digit number)
12041076584947375380…67788428831286403841
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
1.204 Γ— 10⁹⁷(98-digit number)
12041076584947375380…67788428831286403841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.408 Γ— 10⁹⁷(98-digit number)
24082153169894750760…35576857662572807681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.816 Γ— 10⁹⁷(98-digit number)
48164306339789501520…71153715325145615361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.632 Γ— 10⁹⁷(98-digit number)
96328612679579003040…42307430650291230721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.926 Γ— 10⁹⁸(99-digit number)
19265722535915800608…84614861300582461441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.853 Γ— 10⁹⁸(99-digit number)
38531445071831601216…69229722601164922881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.706 Γ— 10⁹⁸(99-digit number)
77062890143663202432…38459445202329845761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.541 Γ— 10⁹⁹(100-digit number)
15412578028732640486…76918890404659691521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.082 Γ— 10⁹⁹(100-digit number)
30825156057465280973…53837780809319383041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.165 Γ— 10⁹⁹(100-digit number)
61650312114930561946…07675561618638766081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.233 Γ— 10¹⁰⁰(101-digit number)
12330062422986112389…15351123237277532161
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:57,991,532 XPMΒ·at block #6,843,395 Β· updates every 60s
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