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Block #569,680

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/31/2014, 7:38:10 AM Β· Difficulty 10.9647 Β· 6,246,524 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
83c32d2b078567ec0d7d197745016f3fbcd93ed50862ba57aad24a75e18cae65
View on Chainz β†—

Height

#569,680

Difficulty

10.964745

Transactions

1

Size

208 B

Version

2

Bits

0af6f984

Nonce

366,233,372

Timestamp

5/31/2014, 7:38:10 AM

Confirmations

6,246,524

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c047acd5f0011dfd97701127400a5e7fb88fc9b3120708ec3a9111790ae3ba28
Transactions (1)
Coinbasec047acd5f0011d…9111790ae3ba28
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.981 Γ— 10⁹⁸(99-digit number)
99813227933840413616…68215528445946636801
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
9.981 Γ— 10⁹⁸(99-digit number)
99813227933840413616…68215528445946636801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.996 Γ— 10⁹⁹(100-digit number)
19962645586768082723…36431056891893273601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.992 Γ— 10⁹⁹(100-digit number)
39925291173536165446…72862113783786547201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.985 Γ— 10⁹⁹(100-digit number)
79850582347072330892…45724227567573094401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.597 Γ— 10¹⁰⁰(101-digit number)
15970116469414466178…91448455135146188801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.194 Γ— 10¹⁰⁰(101-digit number)
31940232938828932357…82896910270292377601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.388 Γ— 10¹⁰⁰(101-digit number)
63880465877657864714…65793820540584755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.277 Γ— 10¹⁰¹(102-digit number)
12776093175531572942…31587641081169510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.555 Γ— 10¹⁰¹(102-digit number)
25552186351063145885…63175282162339020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.110 Γ— 10¹⁰¹(102-digit number)
51104372702126291771…26350564324678041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.022 Γ— 10¹⁰²(103-digit number)
10220874540425258354…52701128649356083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.044 Γ— 10¹⁰²(103-digit number)
20441749080850516708…05402257298712166401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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
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