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Block #437,387

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/10/2014, 6:39:30 AM Β· Difficulty 10.3574 Β· 6,368,636 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e6106ccab99a7bbb5078264129d98ff54583bd959f4e3a4613d96be590b465ee
View on Chainz β†—

Height

#437,387

Difficulty

10.357440

Transactions

1

Size

207 B

Version

2

Bits

0a5b812d

Nonce

1,910

Timestamp

3/10/2014, 6:39:30 AM

Confirmations

6,368,636

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

389f511b03da826b4f3a774599189bb31d5fbec9b1e5f064b3af13fdd1c704e1
Transactions (1)
Coinbase389f511b03da82…af13fdd1c704e1
1 in β†’ 1 out9.3100 XPM116 B
AbwWkWZt…kawDhufa
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.

1.833 Γ— 10⁹⁷(98-digit number)
18333120351843370085…02380422186849164811
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
1.833 Γ— 10⁹⁷(98-digit number)
18333120351843370085…02380422186849164811
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.666 Γ— 10⁹⁷(98-digit number)
36666240703686740170…04760844373698329621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.333 Γ— 10⁹⁷(98-digit number)
73332481407373480340…09521688747396659241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.466 Γ— 10⁹⁸(99-digit number)
14666496281474696068…19043377494793318481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.933 Γ— 10⁹⁸(99-digit number)
29332992562949392136…38086754989586636961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.866 Γ— 10⁹⁸(99-digit number)
58665985125898784272…76173509979173273921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.173 Γ— 10⁹⁹(100-digit number)
11733197025179756854…52347019958346547841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.346 Γ— 10⁹⁹(100-digit number)
23466394050359513709…04694039916693095681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.693 Γ— 10⁹⁹(100-digit number)
46932788100719027418…09388079833386191361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.386 Γ— 10⁹⁹(100-digit number)
93865576201438054836…18776159666772382721
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:57,692,262 XPMΒ·at block #6,806,022 Β· updates every 60s
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