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Block #568,010

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/30/2014, 2:40:07 AM Β· Difficulty 10.9652 Β· 6,228,821 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
13888b1ee700dc9f594deb51cdf740457a5c06e00f9c06df23eb06135bce8ec9
View on Chainz β†—

Height

#568,010

Difficulty

10.965159

Transactions

2

Size

694 B

Version

2

Bits

0af714a8

Nonce

645,930,042

Timestamp

5/30/2014, 2:40:07 AM

Confirmations

6,228,821

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1441baf2cf7f325b2783bb16321c61e6ee28e9ae21e55de3739d7e66425f4a8a
Transactions (2)
Coinbasec298c4a8566a69…08646cf2119151
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
40d1a7fc05aaa9…51fb3e9ced3ec7
3 in β†’ 1 out5.0000 XPM486 B
APg6LYPb…75ZxJ4Sq
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.

1.687 Γ— 10⁹⁸(99-digit number)
16878517001472074939…84664440157582294401
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
1.687 Γ— 10⁹⁸(99-digit number)
16878517001472074939…84664440157582294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.375 Γ— 10⁹⁸(99-digit number)
33757034002944149878…69328880315164588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.751 Γ— 10⁹⁸(99-digit number)
67514068005888299756…38657760630329177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.350 Γ— 10⁹⁹(100-digit number)
13502813601177659951…77315521260658355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.700 Γ— 10⁹⁹(100-digit number)
27005627202355319902…54631042521316710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.401 Γ— 10⁹⁹(100-digit number)
54011254404710639805…09262085042633420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.080 Γ— 10¹⁰⁰(101-digit number)
10802250880942127961…18524170085266841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.160 Γ— 10¹⁰⁰(101-digit number)
21604501761884255922…37048340170533683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.320 Γ— 10¹⁰⁰(101-digit number)
43209003523768511844…74096680341067366401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.641 Γ— 10¹⁰⁰(101-digit number)
86418007047537023688…48193360682134732801
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:57,618,658 XPMΒ·at block #6,796,830 Β· updates every 60s
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