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Block #415,324

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/22/2014, 3:06:39 PM Β· Difficulty 10.4043 Β· 6,392,251 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
86c8ec6e1dfd921d9bef28328aa257e009d8766d34674af44738121efbfb88f3
View on Chainz β†—

Height

#415,324

Difficulty

10.404275

Transactions

2

Size

393 B

Version

2

Bits

0a677e99

Nonce

4,188

Timestamp

2/22/2014, 3:06:39 PM

Confirmations

6,392,251

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

98aa9f659e2810449d04295677c315649b6311b5af15ca92a3a87155dca4d260
Transactions (2)
Coinbasedd5ebb500d62a1…c2868cb0c78678
1 in β†’ 1 out9.2326 XPM110 B
AeKNrjNj…1NEq95Ta
6c7fd7e9a16a20…d1ce9f25443bda
1 in β†’ 1 out2.9900 XPM192 B
AH2Py5dY…6P2kVddD
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.

3.366 Γ— 10⁹⁷(98-digit number)
33664910803070640945…22866330611583127041
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
3.366 Γ— 10⁹⁷(98-digit number)
33664910803070640945…22866330611583127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.732 Γ— 10⁹⁷(98-digit number)
67329821606141281890…45732661223166254081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.346 Γ— 10⁹⁸(99-digit number)
13465964321228256378…91465322446332508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.693 Γ— 10⁹⁸(99-digit number)
26931928642456512756…82930644892665016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.386 Γ— 10⁹⁸(99-digit number)
53863857284913025512…65861289785330032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.077 Γ— 10⁹⁹(100-digit number)
10772771456982605102…31722579570660065281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.154 Γ— 10⁹⁹(100-digit number)
21545542913965210204…63445159141320130561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.309 Γ— 10⁹⁹(100-digit number)
43091085827930420409…26890318282640261121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.618 Γ— 10⁹⁹(100-digit number)
86182171655860840819…53780636565280522241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.723 Γ— 10¹⁰⁰(101-digit number)
17236434331172168163…07561273130561044481
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:57,704,629 XPMΒ·at block #6,807,574 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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