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Block #811,849

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/15/2014, 7:53:59 AM Β· Difficulty 10.9731 Β· 5,991,607 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4a3919b63ba834bfaae436c41003b7f9c44cab9437865597c7de6d2bd147d998
View on Chainz β†—

Height

#811,849

Difficulty

10.973106

Transactions

2

Size

5.77 KB

Version

2

Bits

0af91d74

Nonce

927,125,684

Timestamp

11/15/2014, 7:53:59 AM

Confirmations

5,991,607

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1f7389d66d6bf1ae6c2af3f4de793da333fcb8784bc95282093dd9a745cb4e6a
Transactions (2)
Coinbase934ab23074ec68…9f19c474c2ca18
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
1c3af61b95c740…95692d770916e1
38 in β†’ 2 out50000.0100 XPM5.57 KB
AQmCc7MA…HKV5orEeAe5WFHbn…gBo7rvHr
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.

3.525 Γ— 10⁹⁡(96-digit number)
35259569739172865520…92043445416234383359
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
3.525 Γ— 10⁹⁡(96-digit number)
35259569739172865520…92043445416234383359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.051 Γ— 10⁹⁡(96-digit number)
70519139478345731040…84086890832468766719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.410 Γ— 10⁹⁢(97-digit number)
14103827895669146208…68173781664937533439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.820 Γ— 10⁹⁢(97-digit number)
28207655791338292416…36347563329875066879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.641 Γ— 10⁹⁢(97-digit number)
56415311582676584832…72695126659750133759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁷(98-digit number)
11283062316535316966…45390253319500267519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.256 Γ— 10⁹⁷(98-digit number)
22566124633070633933…90780506639000535039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.513 Γ— 10⁹⁷(98-digit number)
45132249266141267866…81561013278001070079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.026 Γ— 10⁹⁷(98-digit number)
90264498532282535732…63122026556002140159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.805 Γ— 10⁹⁸(99-digit number)
18052899706456507146…26244053112004280319
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:57,671,675 XPMΒ·at block #6,803,455 Β· updates every 60s
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