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Block #863,371

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/22/2014, 11:10:43 AM Β· Difficulty 10.9627 Β· 5,961,576 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c684228feadb67b29d2a5e76953db4e96f9a44b1a79e9f5dc1a573f9a6288efc
View on Chainz β†—

Height

#863,371

Difficulty

10.962749

Transactions

2

Size

8.51 KB

Version

2

Bits

0af676bc

Nonce

694,214,017

Timestamp

12/22/2014, 11:10:43 AM

Confirmations

5,961,576

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6bce3c654118d4a87b98288c6c28b908dec0b539512bb029d5b25cde3dc3584b
Transactions (2)
Coinbase33dd21f1bd38b0…c32b2482057d15
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
5c21048830a281…16e20f5a1ca1ca
57 in β†’ 2 out500.0100 XPM8.31 KB
AJjnK9uC…VreFquR4AKb9NerM…ckmxv1Cr
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.

1.301 Γ— 10⁹⁡(96-digit number)
13017042718972692923…99074327562853956801
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
1.301 Γ— 10⁹⁡(96-digit number)
13017042718972692923…99074327562853956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.603 Γ— 10⁹⁡(96-digit number)
26034085437945385846…98148655125707913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.206 Γ— 10⁹⁡(96-digit number)
52068170875890771693…96297310251415827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.041 Γ— 10⁹⁢(97-digit number)
10413634175178154338…92594620502831654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.082 Γ— 10⁹⁢(97-digit number)
20827268350356308677…85189241005663308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.165 Γ— 10⁹⁢(97-digit number)
41654536700712617354…70378482011326617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.330 Γ— 10⁹⁢(97-digit number)
83309073401425234709…40756964022653235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.666 Γ— 10⁹⁷(98-digit number)
16661814680285046941…81513928045306470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.332 Γ— 10⁹⁷(98-digit number)
33323629360570093883…63027856090612940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.664 Γ— 10⁹⁷(98-digit number)
66647258721140187767…26055712181225881601
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:57,843,653 XPMΒ·at block #6,824,946 Β· updates every 60s
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