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Block #2,082,912

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/22/2017, 3:37:27 PM Β· Difficulty 10.8702 Β· 4,748,716 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b798116d609ddf89ed458543b8252a806820cd893829ae039e52ae96f15f0f51
View on Chainz β†—

Height

#2,082,912

Difficulty

10.870206

Transactions

2

Size

1.25 KB

Version

2

Bits

0adec5ca

Nonce

683,370,263

Timestamp

4/22/2017, 3:37:27 PM

Confirmations

4,748,716

Mined by

⛏️ P2SHAGqPtmsSLSsbTnMFvc4o7ctAe5GUANKJAE

Merkle Root

7bc756eab7202741a907d6ef92259b373eefeb83b4a1aaeddbd36f628e777238
Transactions (2)
Coinbasef7b049c7c66b65…97528e1cfceae6
1 in β†’ 1 out8.4700 XPM110 B
AGqPtmsS…GUANKJAE
2fd0cfefd63914…c7b38c6a827349
7 in β†’ 1 out558.2700 XPM1.05 KB
AMru4SrA…VW3392hn
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.

6.138 Γ— 10⁹³(94-digit number)
61388783418733581465…56046422883344616959
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
6.138 Γ— 10⁹³(94-digit number)
61388783418733581465…56046422883344616959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁴(95-digit number)
12277756683746716293…12092845766689233919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.455 Γ— 10⁹⁴(95-digit number)
24555513367493432586…24185691533378467839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.911 Γ— 10⁹⁴(95-digit number)
49111026734986865172…48371383066756935679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.822 Γ— 10⁹⁴(95-digit number)
98222053469973730344…96742766133513871359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.964 Γ— 10⁹⁡(96-digit number)
19644410693994746068…93485532267027742719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.928 Γ— 10⁹⁡(96-digit number)
39288821387989492137…86971064534055485439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.857 Γ— 10⁹⁡(96-digit number)
78577642775978984275…73942129068110970879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.571 Γ— 10⁹⁢(97-digit number)
15715528555195796855…47884258136221941759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.143 Γ— 10⁹⁢(97-digit number)
31431057110391593710…95768516272443883519
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:57,897,126 XPMΒ·at block #6,831,627 Β· updates every 60s
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