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Block #860,819

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/20/2014, 1:32:41 PM Β· Difficulty 10.9640 Β· 5,972,093 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0266e81e44c1dd463423759d9214171c8d282450523511b9d600ec796256c622
View on Chainz β†—

Height

#860,819

Difficulty

10.964005

Transactions

2

Size

26.43 KB

Version

2

Bits

0af6c908

Nonce

1,225,109,295

Timestamp

12/20/2014, 1:32:41 PM

Confirmations

5,972,093

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0123774068a6effcdf0f1bb084dc0e2d59d68eb00f8ec1742802672e03b8ba82
Transactions (2)
Coinbase8c5dce917d6566…81a3e7b550201a
1 in β†’ 1 out8.5800 XPM116 B
ANSXnLY2…Sd25TjkD
99cdc96a6374ad…86f5f3de3d1a18
181 in β†’ 2 out1.6748 XPM26.23 KB
AW32SVdm…WAR9atiTAeB8EJC3…dGo5s9t5
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.

1.132 Γ— 10⁹⁡(96-digit number)
11323099427561045894…89533441352138101761
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
1.132 Γ— 10⁹⁡(96-digit number)
11323099427561045894…89533441352138101761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.264 Γ— 10⁹⁡(96-digit number)
22646198855122091789…79066882704276203521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.529 Γ— 10⁹⁡(96-digit number)
45292397710244183578…58133765408552407041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.058 Γ— 10⁹⁡(96-digit number)
90584795420488367157…16267530817104814081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.811 Γ— 10⁹⁢(97-digit number)
18116959084097673431…32535061634209628161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.623 Γ— 10⁹⁢(97-digit number)
36233918168195346863…65070123268419256321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.246 Γ— 10⁹⁢(97-digit number)
72467836336390693726…30140246536838512641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.449 Γ— 10⁹⁷(98-digit number)
14493567267278138745…60280493073677025281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.898 Γ— 10⁹⁷(98-digit number)
28987134534556277490…20560986147354050561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.797 Γ— 10⁹⁷(98-digit number)
57974269069112554980…41121972294708101121
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:57,907,468 XPMΒ·at block #6,832,911 Β· updates every 60s
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