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Block #2,633,801

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 2:59:56 PM Β· Difficulty 11.2088 Β· 4,206,426 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68462427fa6c9b533b3c8db548a9f91d63eeca8e6a1eeeefa83196eba840d91c
View on Chainz β†—

Height

#2,633,801

Difficulty

11.208815

Transactions

1

Size

200 B

Version

2

Bits

0b3574e1

Nonce

66,248,051

Timestamp

4/28/2018, 2:59:56 PM

Confirmations

4,206,426

Mined by

⛏️ P2SHANizfXWtZmMJQgnmSz8KHnXqWe3k5NWH3e

Merkle Root

2502099f6cbe7c1687d2ada7459f8e7ba15378babd822cd8e8b9124fabf2e39a
Transactions (1)
Coinbase2502099f6cbe7c…b9124fabf2e39a
1 in β†’ 1 out7.9500 XPM110 B
ANizfXWt…3k5NWH3e
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.

1.804 Γ— 10⁹⁡(96-digit number)
18042279568710722214…42595485070274949121
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
1.804 Γ— 10⁹⁡(96-digit number)
18042279568710722214…42595485070274949121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.608 Γ— 10⁹⁡(96-digit number)
36084559137421444428…85190970140549898241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.216 Γ— 10⁹⁡(96-digit number)
72169118274842888857…70381940281099796481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.443 Γ— 10⁹⁢(97-digit number)
14433823654968577771…40763880562199592961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.886 Γ— 10⁹⁢(97-digit number)
28867647309937155543…81527761124399185921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.773 Γ— 10⁹⁢(97-digit number)
57735294619874311086…63055522248798371841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.154 Γ— 10⁹⁷(98-digit number)
11547058923974862217…26111044497596743681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.309 Γ— 10⁹⁷(98-digit number)
23094117847949724434…52222088995193487361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.618 Γ— 10⁹⁷(98-digit number)
46188235695899448868…04444177990386974721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.237 Γ— 10⁹⁷(98-digit number)
92376471391798897737…08888355980773949441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.847 Γ— 10⁹⁸(99-digit number)
18475294278359779547…17776711961547898881
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:57,966,128 XPMΒ·at block #6,840,226 Β· updates every 60s
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