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Block #292,155

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/3/2013, 2:12:13 PM Β· Difficulty 9.9902 Β· 6,533,437 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
89bbf9f5921403579d43f2008f91ba13950521aba64d7be7a59a7fe1f98532b4
View on Chainz β†—

Height

#292,155

Difficulty

9.990159

Transactions

1

Size

210 B

Version

2

Bits

09fd7b09

Nonce

2,840

Timestamp

12/3/2013, 2:12:13 PM

Confirmations

6,533,437

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

900e4aa201a512530192c05384934dcd13c60da4104a6a69986bd746a4b89c84
Transactions (1)
Coinbase900e4aa201a512…6bd746a4b89c84
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.427 Γ— 10¹⁰³(104-digit number)
24279914410744866872…74208306045381509119
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
2.427 Γ— 10¹⁰³(104-digit number)
24279914410744866872…74208306045381509119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.855 Γ— 10¹⁰³(104-digit number)
48559828821489733744…48416612090763018239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.711 Γ— 10¹⁰³(104-digit number)
97119657642979467488…96833224181526036479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.942 Γ— 10¹⁰⁴(105-digit number)
19423931528595893497…93666448363052072959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.884 Γ— 10¹⁰⁴(105-digit number)
38847863057191786995…87332896726104145919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.769 Γ— 10¹⁰⁴(105-digit number)
77695726114383573990…74665793452208291839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.553 Γ— 10¹⁰⁡(106-digit number)
15539145222876714798…49331586904416583679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.107 Γ— 10¹⁰⁡(106-digit number)
31078290445753429596…98663173808833167359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.215 Γ— 10¹⁰⁡(106-digit number)
62156580891506859192…97326347617666334719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.243 Γ— 10¹⁰⁢(107-digit number)
12431316178301371838…94652695235332669439
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:57,848,836 XPMΒ·at block #6,825,591 Β· updates every 60s
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