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Block #2,873,518

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/9/2018, 4:02:48 AM Β· Difficulty 11.6657 Β· 3,969,530 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31c5b555874e94a716865d935c3d56b84f89827315c27d6fc0e292c3429bfa45
View on Chainz β†—

Height

#2,873,518

Difficulty

11.665671

Transactions

2

Size

574 B

Version

2

Bits

0baa696e

Nonce

651,294,135

Timestamp

10/9/2018, 4:02:48 AM

Confirmations

3,969,530

Mined by

⛏️ P2SHASCs3QeZaZtW7ukcTJ7LhAbUuh6Q5pRzCS

Merkle Root

965cf72dfef49aa63d8ebd3da6d108c3f773c18dc1c48d88df203de2a8b3a73d
Transactions (2)
Coinbase7da700e64d00e7…9293fa8b983215
1 in β†’ 1 out7.3500 XPM109 B
ASCs3QeZ…6Q5pRzCS
46df414769478b…13c4b38b5ed7d0
2 in β†’ 2 out19.9900 XPM375 B
AWWCieH1…sLoR4q6tAPSdSs6C…Ukaxq6S9
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.

1.071 Γ— 10⁹⁴(95-digit number)
10719782952309083084…40001896660138301039
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
1.071 Γ— 10⁹⁴(95-digit number)
10719782952309083084…40001896660138301039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁴(95-digit number)
21439565904618166168…80003793320276602079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.287 Γ— 10⁹⁴(95-digit number)
42879131809236332337…60007586640553204159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.575 Γ— 10⁹⁴(95-digit number)
85758263618472664674…20015173281106408319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.715 Γ— 10⁹⁡(96-digit number)
17151652723694532934…40030346562212816639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.430 Γ— 10⁹⁡(96-digit number)
34303305447389065869…80060693124425633279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.860 Γ— 10⁹⁡(96-digit number)
68606610894778131739…60121386248851266559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.372 Γ— 10⁹⁢(97-digit number)
13721322178955626347…20242772497702533119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.744 Γ— 10⁹⁢(97-digit number)
27442644357911252695…40485544995405066239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.488 Γ— 10⁹⁢(97-digit number)
54885288715822505391…80971089990810132479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁷(98-digit number)
10977057743164501078…61942179981620264959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,988,742 XPMΒ·at block #6,843,047 Β· updates every 60s
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