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Block #295,281

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 8:44:43 AM Β· Difficulty 9.9913 Β· 6,522,413 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
79c04cf07c9ce1e03a0ea25421c2bb0b2280217c93fa4476aa164a0a821e8079
View on Chainz β†—

Height

#295,281

Difficulty

9.991320

Transactions

1

Size

210 B

Version

2

Bits

09fdc72a

Nonce

9,939

Timestamp

12/5/2013, 8:44:43 AM

Confirmations

6,522,413

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

227c3830f8d272e3052a7dde3cf0f7a3adfdc791119769bab6631f3c1ce85e1a
Transactions (1)
Coinbase227c3830f8d272…631f3c1ce85e1a
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.

2.980 Γ— 10¹⁰⁴(105-digit number)
29804318517605905497…81643379036551905279
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
2.980 Γ— 10¹⁰⁴(105-digit number)
29804318517605905497…81643379036551905279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.960 Γ— 10¹⁰⁴(105-digit number)
59608637035211810995…63286758073103810559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.192 Γ— 10¹⁰⁡(106-digit number)
11921727407042362199…26573516146207621119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.384 Γ— 10¹⁰⁡(106-digit number)
23843454814084724398…53147032292415242239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.768 Γ— 10¹⁰⁡(106-digit number)
47686909628169448796…06294064584830484479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.537 Γ— 10¹⁰⁡(106-digit number)
95373819256338897592…12588129169660968959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.907 Γ— 10¹⁰⁢(107-digit number)
19074763851267779518…25176258339321937919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.814 Γ— 10¹⁰⁢(107-digit number)
38149527702535559037…50352516678643875839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.629 Γ— 10¹⁰⁢(107-digit number)
76299055405071118074…00705033357287751679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.525 Γ— 10¹⁰⁷(108-digit number)
15259811081014223614…01410066714575503359
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:57,785,610 XPMΒ·at block #6,817,693 Β· updates every 60s
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