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Block #2,116,719

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/15/2017, 1:52:34 AM Β· Difficulty 10.9047 Β· 4,710,394 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ffe008845df6c1ef74f3812c20253a09d6d4dc413d716235061709037c979cf9
View on Chainz β†—

Height

#2,116,719

Difficulty

10.904702

Transactions

2

Size

4.03 KB

Version

2

Bits

0ae79a94

Nonce

90,243,594

Timestamp

5/15/2017, 1:52:34 AM

Confirmations

4,710,394

Mined by

⛏️ P2SHAczBHZ6zGprNaajfxRt5tVkD6fenveKHRN

Merkle Root

f9d99de0157eecfaa0866475dc169fc9992b161e4f089603d9f2cafabb351d2b
Transactions (2)
Coinbase3c25a5b225b08d…803815011879c2
1 in β†’ 1 out8.4400 XPM110 B
AczBHZ6z…enveKHRN
d22096e7b14aa1…c6bdd48874326a
26 in β†’ 2 out99.8763 XPM3.84 KB
AKGxoSP8…8oH3hVLdAaWiVovJ…rt39wtus
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.

1.192 Γ— 10⁹³(94-digit number)
11929786185381138732…73654498849349452599
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
1.192 Γ— 10⁹³(94-digit number)
11929786185381138732…73654498849349452599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.385 Γ— 10⁹³(94-digit number)
23859572370762277464…47308997698698905199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.771 Γ— 10⁹³(94-digit number)
47719144741524554928…94617995397397810399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.543 Γ— 10⁹³(94-digit number)
95438289483049109857…89235990794795620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁴(95-digit number)
19087657896609821971…78471981589591241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.817 Γ— 10⁹⁴(95-digit number)
38175315793219643942…56943963179182483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.635 Γ— 10⁹⁴(95-digit number)
76350631586439287885…13887926358364966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.527 Γ— 10⁹⁡(96-digit number)
15270126317287857577…27775852716729932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.054 Γ— 10⁹⁡(96-digit number)
30540252634575715154…55551705433459865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.108 Γ— 10⁹⁡(96-digit number)
61080505269151430308…11103410866919731199
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:57,861,083 XPMΒ·at block #6,827,112 Β· updates every 60s
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