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Block #1,316,345

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/7/2015, 2:03:47 AM Β· Difficulty 10.8623 Β· 5,501,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df9bd7b04e261164c4b2ac673994ba43c0236f39d95297db893f13f5950067b8
View on Chainz β†—

Height

#1,316,345

Difficulty

10.862292

Transactions

2

Size

5.15 KB

Version

2

Bits

0adcbf2e

Nonce

64,094,774

Timestamp

11/7/2015, 2:03:47 AM

Confirmations

5,501,143

Mined by

⛏️ P2SHAVxGe5uY2Emsv725X4FLSPbcAj2WSkLaUL

Merkle Root

712ae170a85927d50c57e6a9dad16ded757a3d6e5b4a1b13956d53daf15b96d4
Transactions (2)
Coinbase927d92f98d84c2…b1b4cb24bdd00f
1 in β†’ 1 out8.5200 XPM110 B
AVxGe5uY…2WSkLaUL
5b54613aaa810b…b9dfbc61ef43eb
34 in β†’ 1 out72.2629 XPM4.96 KB
AHJeiJjZ…AtVjQXra
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.

9.806 Γ— 10⁹⁴(95-digit number)
98060706462796558780…10637333475074565441
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
9.806 Γ— 10⁹⁴(95-digit number)
98060706462796558780…10637333475074565441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.961 Γ— 10⁹⁡(96-digit number)
19612141292559311756…21274666950149130881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.922 Γ— 10⁹⁡(96-digit number)
39224282585118623512…42549333900298261761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.844 Γ— 10⁹⁡(96-digit number)
78448565170237247024…85098667800596523521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.568 Γ— 10⁹⁢(97-digit number)
15689713034047449404…70197335601193047041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.137 Γ— 10⁹⁢(97-digit number)
31379426068094898809…40394671202386094081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.275 Γ— 10⁹⁢(97-digit number)
62758852136189797619…80789342404772188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.255 Γ— 10⁹⁷(98-digit number)
12551770427237959523…61578684809544376321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.510 Γ— 10⁹⁷(98-digit number)
25103540854475919047…23157369619088752641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.020 Γ— 10⁹⁷(98-digit number)
50207081708951838095…46314739238177505281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,783,959 XPMΒ·at block #6,817,487 Β· updates every 60s
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