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Block #845,628

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/9/2014, 12:36:05 AM Β· Difficulty 10.9725 Β· 5,996,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c4a3b7495d641c1a54fbca7bdcc796371a30e74212a9d8875be955f200dc720
View on Chainz β†—

Height

#845,628

Difficulty

10.972454

Transactions

1

Size

206 B

Version

2

Bits

0af8f2ba

Nonce

999,824,920

Timestamp

12/9/2014, 12:36:05 AM

Confirmations

5,996,400

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

91ecfe62ae2454c77c3899ddf8ff1cb0cbfbf355ae7b708075aacc6b1960b249
Transactions (1)
Coinbase91ecfe62ae2454…aacc6b1960b249
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.047 Γ— 10⁹⁴(95-digit number)
30470895746961508706…71900087115013801061
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
3.047 Γ— 10⁹⁴(95-digit number)
30470895746961508706…71900087115013801061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.094 Γ— 10⁹⁴(95-digit number)
60941791493923017412…43800174230027602121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.218 Γ— 10⁹⁡(96-digit number)
12188358298784603482…87600348460055204241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.437 Γ— 10⁹⁡(96-digit number)
24376716597569206965…75200696920110408481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.875 Γ— 10⁹⁡(96-digit number)
48753433195138413930…50401393840220816961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.750 Γ— 10⁹⁡(96-digit number)
97506866390276827860…00802787680441633921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.950 Γ— 10⁹⁢(97-digit number)
19501373278055365572…01605575360883267841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.900 Γ— 10⁹⁢(97-digit number)
39002746556110731144…03211150721766535681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.800 Γ— 10⁹⁢(97-digit number)
78005493112221462288…06422301443533071361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.560 Γ— 10⁹⁷(98-digit number)
15601098622444292457…12844602887066142721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.120 Γ— 10⁹⁷(98-digit number)
31202197244888584915…25689205774132285441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,980,610 XPMΒ·at block #6,842,027 Β· updates every 60s
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