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Block #420,167

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/26/2014, 5:16:20 AM Β· Difficulty 10.3669 Β· 6,376,052 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed20285d1a80f385fd56049ea3f2490b7f1ea0a5fd5b59209de73a45c6ab5535
View on Chainz β†—

Height

#420,167

Difficulty

10.366859

Transactions

1

Size

190 B

Version

2

Bits

0a5dea80

Nonce

315,898

Timestamp

2/26/2014, 5:16:20 AM

Confirmations

6,376,052

Mined by

⛏️ P2SHAaXb6LdzMFohbBjmNyta5dnWNNXefG91jF

Merkle Root

02e4f7d32df5d65765631a5233604f5bc59a6e9e210562d5748b7ae8fd7f270b
Transactions (1)
Coinbase02e4f7d32df5d6…8b7ae8fd7f270b
1 in β†’ 1 out9.2900 XPM100 B
AaXb6Ldz…XefG91jF
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.

1.253 Γ— 10⁹⁡(96-digit number)
12539059778032564410…52205217947049976141
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
1.253 Γ— 10⁹⁡(96-digit number)
12539059778032564410…52205217947049976141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.507 Γ— 10⁹⁡(96-digit number)
25078119556065128821…04410435894099952281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.015 Γ— 10⁹⁡(96-digit number)
50156239112130257643…08820871788199904561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.003 Γ— 10⁹⁢(97-digit number)
10031247822426051528…17641743576399809121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.006 Γ— 10⁹⁢(97-digit number)
20062495644852103057…35283487152799618241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.012 Γ— 10⁹⁢(97-digit number)
40124991289704206114…70566974305599236481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.024 Γ— 10⁹⁢(97-digit number)
80249982579408412229…41133948611198472961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.604 Γ— 10⁹⁷(98-digit number)
16049996515881682445…82267897222396945921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.209 Γ— 10⁹⁷(98-digit number)
32099993031763364891…64535794444793891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.419 Γ— 10⁹⁷(98-digit number)
64199986063526729783…29071588889587783681
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:57,613,745 XPMΒ·at block #6,796,218 Β· updates every 60s
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