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Block #600,114

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/24/2014, 6:43:07 AM Β· Difficulty 10.9229 Β· 6,205,579 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d399e9d29b7be0c3e4df2de375d56d104e6a014e3ef13cac5b741a17b7400d37
View on Chainz β†—

Height

#600,114

Difficulty

10.922884

Transactions

2

Size

1.27 KB

Version

2

Bits

0aec4226

Nonce

663,504

Timestamp

6/24/2014, 6:43:07 AM

Confirmations

6,205,579

Mined by

AWQBKr3YBNqdknh157YGqdQEjQsUA1Ehpd

Merkle Root

7e9d5b114f2fca0c18c120793a1ddcda31a315bc4c1914ab9dabe8869d71e881
Transactions (2)
Coinbase397cc70ea89612…a88dbfb99e4f20
1 in β†’ 1 out8.3700 XPM96 B
AWQBKr3Y…sUA1Ehpd
c3b59f9ff939d3…c59974e4b5f7a3
7 in β†’ 2 out40.2621 XPM1.09 KB
ANdX2bVa…FBx1DAUHAW6Cei3u…fGJvgpw8
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.

2.736 Γ— 10⁹²(93-digit number)
27366148768951179059…30346881241944344961
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
2.736 Γ— 10⁹²(93-digit number)
27366148768951179059…30346881241944344961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.473 Γ— 10⁹²(93-digit number)
54732297537902358118…60693762483888689921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.094 Γ— 10⁹³(94-digit number)
10946459507580471623…21387524967777379841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.189 Γ— 10⁹³(94-digit number)
21892919015160943247…42775049935554759681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.378 Γ— 10⁹³(94-digit number)
43785838030321886494…85550099871109519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.757 Γ— 10⁹³(94-digit number)
87571676060643772989…71100199742219038721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.751 Γ— 10⁹⁴(95-digit number)
17514335212128754597…42200399484438077441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.502 Γ— 10⁹⁴(95-digit number)
35028670424257509195…84400798968876154881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.005 Γ— 10⁹⁴(95-digit number)
70057340848515018391…68801597937752309761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.401 Γ— 10⁹⁡(96-digit number)
14011468169703003678…37603195875504619521
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:57,689,626 XPMΒ·at block #6,805,692 Β· updates every 60s
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