XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,093,900

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2017, 6:25:34 AM Β· Difficulty 10.8711 Β· 4,718,874 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b41d154819d0bb1f2ecf3b9e9ac34f7d996843d9644a9fc51db5d9a6ed35e359
View on Chainz β†—

Height

#2,093,900

Difficulty

10.871116

Transactions

2

Size

1.72 KB

Version

2

Bits

0adf0175

Nonce

1,313,512,487

Timestamp

4/30/2017, 6:25:34 AM

Confirmations

4,718,874

Mined by

⛏️ P2SHALp63EFLPWbhciW9XGLC2PLhTSnWKnEKxz

Merkle Root

23252d7e46eb93576d53f2454d6d84e8231ed530ce6cbd909cf0f77d0119ad4f
Transactions (2)
Coinbase958189bc165575…4e5f6210f3b230
1 in β†’ 1 out8.4700 XPM109 B
ALp63EFL…nWKnEKxz
06897c9d931c14…c190cbadf474d3
10 in β†’ 2 out415.8216 XPM1.52 KB
AJvNytu2…1LqXJ7ESAWZWPLV8…xrguMbe3
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.

9.980 Γ— 10⁹⁢(97-digit number)
99806585556005499877…42100513910204364801
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
9.980 Γ— 10⁹⁢(97-digit number)
99806585556005499877…42100513910204364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.996 Γ— 10⁹⁷(98-digit number)
19961317111201099975…84201027820408729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.992 Γ— 10⁹⁷(98-digit number)
39922634222402199951…68402055640817459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.984 Γ— 10⁹⁷(98-digit number)
79845268444804399902…36804111281634918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.596 Γ— 10⁹⁸(99-digit number)
15969053688960879980…73608222563269836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.193 Γ— 10⁹⁸(99-digit number)
31938107377921759960…47216445126539673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.387 Γ— 10⁹⁸(99-digit number)
63876214755843519921…94432890253079347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.277 Γ— 10⁹⁹(100-digit number)
12775242951168703984…88865780506158694401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.555 Γ— 10⁹⁹(100-digit number)
25550485902337407968…77731561012317388801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.110 Γ— 10⁹⁹(100-digit number)
51100971804674815937…55463122024634777601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.022 Γ— 10¹⁰⁰(101-digit number)
10220194360934963187…10926244049269555201
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:57,746,231 XPMΒ·at block #6,812,773 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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