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Block #407,070

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/16/2014, 5:52:32 PM Β· Difficulty 10.4326 Β· 6,403,638 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d380baa734ea8cf6ff77f4a9f169536799f846d1eb0968236a285011fbff1027
View on Chainz β†—

Height

#407,070

Difficulty

10.432550

Transactions

2

Size

1.14 KB

Version

2

Bits

0a6ebb9f

Nonce

47,697

Timestamp

2/16/2014, 5:52:32 PM

Confirmations

6,403,638

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

df502a0beeb390677a3704ac5b3cc22f8ef263ba503e0f28e8d575f5b5df0cdd
Transactions (2)
Coinbasedffaf415fafbea…653748b202591f
1 in β†’ 1 out9.1800 XPM110 B
AeKNrjNj…1NEq95Ta
a6b904c8503334…b3b310a4369b42
6 in β†’ 2 out35.2222 XPM969 B
AKVujRA8…3pDvRVMeAGogVkh9…jxtJ94Xj
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.

1.111 Γ— 10⁹⁷(98-digit number)
11118002537077569473…41762459386435972281
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
1.111 Γ— 10⁹⁷(98-digit number)
11118002537077569473…41762459386435972281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.223 Γ— 10⁹⁷(98-digit number)
22236005074155138946…83524918772871944561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.447 Γ— 10⁹⁷(98-digit number)
44472010148310277892…67049837545743889121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.894 Γ— 10⁹⁷(98-digit number)
88944020296620555784…34099675091487778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.778 Γ— 10⁹⁸(99-digit number)
17788804059324111156…68199350182975556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.557 Γ— 10⁹⁸(99-digit number)
35577608118648222313…36398700365951112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.115 Γ— 10⁹⁸(99-digit number)
71155216237296444627…72797400731902225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.423 Γ— 10⁹⁹(100-digit number)
14231043247459288925…45594801463804451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.846 Γ— 10⁹⁹(100-digit number)
28462086494918577851…91189602927608903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.692 Γ— 10⁹⁹(100-digit number)
56924172989837155702…82379205855217807361
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:57,729,750 XPMΒ·at block #6,810,707 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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