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Block #491,869

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/14/2014, 6:33:02 PM Β· Difficulty 10.6858 Β· 6,303,682 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0984676ed589af9039402e3ecc9e1f6791d55da07560238e8e7e55a078f3afa0
View on Chainz β†—

Height

#491,869

Difficulty

10.685802

Transactions

1

Size

200 B

Version

2

Bits

0aaf90b4

Nonce

73,991

Timestamp

4/14/2014, 6:33:02 PM

Confirmations

6,303,682

Mined by

⛏️ P2SHAdPiCUaFgvhjwm1yZha2oPgWJehRPkRNeG

Merkle Root

15a9d59842b77ee437328a8ad9a1e77ad7d7e66ee519649064b989aacd770188
Transactions (1)
Coinbase15a9d59842b77e…b989aacd770188
1 in β†’ 1 out8.7400 XPM110 B
AdPiCUaF…hRPkRNeG
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.

4.351 Γ— 10⁹⁡(96-digit number)
43510324227993290210…28242280718959925001
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
4.351 Γ— 10⁹⁡(96-digit number)
43510324227993290210…28242280718959925001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.702 Γ— 10⁹⁡(96-digit number)
87020648455986580420…56484561437919850001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.740 Γ— 10⁹⁢(97-digit number)
17404129691197316084…12969122875839700001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.480 Γ— 10⁹⁢(97-digit number)
34808259382394632168…25938245751679400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.961 Γ— 10⁹⁢(97-digit number)
69616518764789264336…51876491503358800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.392 Γ— 10⁹⁷(98-digit number)
13923303752957852867…03752983006717600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.784 Γ— 10⁹⁷(98-digit number)
27846607505915705734…07505966013435200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.569 Γ— 10⁹⁷(98-digit number)
55693215011831411468…15011932026870400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.113 Γ— 10⁹⁸(99-digit number)
11138643002366282293…30023864053740800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.227 Γ— 10⁹⁸(99-digit number)
22277286004732564587…60047728107481600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.455 Γ— 10⁹⁸(99-digit number)
44554572009465129175…20095456214963200001
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:57,608,472 XPMΒ·at block #6,795,550 Β· updates every 60s
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