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Block #236,292

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/31/2013, 10:26:23 AM Β· Difficulty 9.9471 Β· 6,579,641 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d90d8dd7e98d3d87b71db985c2d28431ff31d51a8d32ec59f0fbcb8684934952
View on Chainz β†—

Height

#236,292

Difficulty

9.947054

Transactions

2

Size

540 B

Version

2

Bits

09f27225

Nonce

2,542

Timestamp

10/31/2013, 10:26:23 AM

Confirmations

6,579,641

Mined by

⛏️ P2SHAWKLbdikDJBNwg6tqhSF566ybZA4VMuxRe

Merkle Root

c5cee15b92f76be9cb127f04d49cf9934c48f19cd4573361a0d00132480dd543
Transactions (2)
Coinbaseef36307301f110…292765ec1b50a9
1 in β†’ 1 out10.1000 XPM109 B
AWKLbdik…A4VMuxRe
6508813427865a…e7637d63f00948
2 in β†’ 1 out0.3856 XPM341 B
AY4JWMsH…b9s1QxQq
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.

7.842 Γ— 10⁹⁴(95-digit number)
78429983885278449294…59913606973317117441
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
7.842 Γ— 10⁹⁴(95-digit number)
78429983885278449294…59913606973317117441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.568 Γ— 10⁹⁡(96-digit number)
15685996777055689858…19827213946634234881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.137 Γ— 10⁹⁡(96-digit number)
31371993554111379717…39654427893268469761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.274 Γ— 10⁹⁡(96-digit number)
62743987108222759435…79308855786536939521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.254 Γ— 10⁹⁢(97-digit number)
12548797421644551887…58617711573073879041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.509 Γ— 10⁹⁢(97-digit number)
25097594843289103774…17235423146147758081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.019 Γ— 10⁹⁢(97-digit number)
50195189686578207548…34470846292295516161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.003 Γ— 10⁹⁷(98-digit number)
10039037937315641509…68941692584591032321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.007 Γ— 10⁹⁷(98-digit number)
20078075874631283019…37883385169182064641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.015 Γ— 10⁹⁷(98-digit number)
40156151749262566038…75766770338364129281
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:57,771,576 XPMΒ·at block #6,815,932 Β· updates every 60s
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