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Block #298,033

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/7/2013, 1:16:17 AM Β· Difficulty 9.9919 Β· 6,497,588 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
214be771aba0d8c780779587ab4771b399c95f84813955a47ebcc666c56db665
View on Chainz β†—

Height

#298,033

Difficulty

9.991939

Transactions

1

Size

1.05 KB

Version

2

Bits

09fdefbb

Nonce

28,947

Timestamp

12/7/2013, 1:16:17 AM

Confirmations

6,497,588

Mined by

⛏️ 1aRvARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

2fdef73490def9c4e5a8a881a45b313f6b79e04b8c77d698a32ca0ad5de8f6ca
Transactions (1)
Coinbase2fdef73490def9…2ca0ad5de8f6ca
1 in β†’ 27 out10.0000 XPM981 B
ARzXge7S…CEjL5oYmAKEwr54i…9BfmMkRhAd9pSzHt…cpJ3y2zzAQwRN8bE…V8PsTcY9AZ2pPuKg…95SN2Yr7
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.

5.644 Γ— 10⁹³(94-digit number)
56443890274025129925…88838584398257826519
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.644 Γ— 10⁹³(94-digit number)
56443890274025129925…88838584398257826519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁴(95-digit number)
11288778054805025985…77677168796515653039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.257 Γ— 10⁹⁴(95-digit number)
22577556109610051970…55354337593031306079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.515 Γ— 10⁹⁴(95-digit number)
45155112219220103940…10708675186062612159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.031 Γ— 10⁹⁴(95-digit number)
90310224438440207880…21417350372125224319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.806 Γ— 10⁹⁡(96-digit number)
18062044887688041576…42834700744250448639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.612 Γ— 10⁹⁡(96-digit number)
36124089775376083152…85669401488500897279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.224 Γ— 10⁹⁡(96-digit number)
72248179550752166304…71338802977001794559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.444 Γ— 10⁹⁢(97-digit number)
14449635910150433260…42677605954003589119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.889 Γ— 10⁹⁢(97-digit number)
28899271820300866521…85355211908007178239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,609,034 XPMΒ·at block #6,795,620 Β· updates every 60s
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