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Block #613,882

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/3/2014, 7:27:59 AM Β· Difficulty 10.9340 Β· 6,195,740 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
759c865ab6fac7d83f3263374699a78bb3a02278e9aa120ecee8df176813290a
View on Chainz β†—

Height

#613,882

Difficulty

10.934011

Transactions

2

Size

21.10 KB

Version

2

Bits

0aef1b59

Nonce

275,437,004

Timestamp

7/3/2014, 7:27:59 AM

Confirmations

6,195,740

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3d5f07bab0c13984915ee8d25b18f6c8a5dbda39489a433c7bbf820fd010aa9c
Transactions (2)
Coinbase8b24c2b3785f44…eb7e2a286d3fd8
1 in β†’ 1 out8.5700 XPM116 B
ANSXnLY2…Sd25TjkD
66bd22757fdb12…89b0e8619501f1
144 in β†’ 2 out500.0106 XPM20.90 KB
AJjnK9uC…VreFquR4AN6H7pEC…YGp6SHhJ
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.

4.114 Γ— 10⁹⁢(97-digit number)
41149953273418207113…37057086964058043201
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
4.114 Γ— 10⁹⁢(97-digit number)
41149953273418207113…37057086964058043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.229 Γ— 10⁹⁢(97-digit number)
82299906546836414226…74114173928116086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.645 Γ— 10⁹⁷(98-digit number)
16459981309367282845…48228347856232172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.291 Γ— 10⁹⁷(98-digit number)
32919962618734565690…96456695712464345601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.583 Γ— 10⁹⁷(98-digit number)
65839925237469131380…92913391424928691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.316 Γ— 10⁹⁸(99-digit number)
13167985047493826276…85826782849857382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.633 Γ— 10⁹⁸(99-digit number)
26335970094987652552…71653565699714764801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.267 Γ— 10⁹⁸(99-digit number)
52671940189975305104…43307131399429529601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.053 Γ— 10⁹⁹(100-digit number)
10534388037995061020…86614262798859059201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.106 Γ— 10⁹⁹(100-digit number)
21068776075990122041…73228525597718118401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.213 Γ— 10⁹⁹(100-digit number)
42137552151980244083…46457051195436236801
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:57,721,054 XPMΒ·at block #6,809,621 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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