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Block #2,784,164

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2018, 1:51:38 AM Β· Difficulty 11.6662 Β· 4,054,064 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
81ab5210bd6ad451843de39a15a5e5848478b5642d0f508a9762924da644ae1c
View on Chainz β†—

Height

#2,784,164

Difficulty

11.666239

Transactions

2

Size

575 B

Version

2

Bits

0baa8ea1

Nonce

771,058,957

Timestamp

8/8/2018, 1:51:38 AM

Confirmations

4,054,064

Mined by

⛏️ P2SHALZ1jMUjj1xM4zrYKkXMLDY4eS9BSbGMnr

Merkle Root

5bb4393978d28d1611581f0825de97b44cf3cdabea536adc0a183d907c7673b0
Transactions (2)
Coinbase9d9475f19e3b03…b9663952b82ca8
1 in β†’ 1 out7.3500 XPM110 B
ALZ1jMUj…9BSbGMnr
df68ab47d6a311…1a4a669cdb9f78
2 in β†’ 2 out7.9900 XPM374 B
ALuyYi5d…VXnE9Z3EAdAay23G…F1TbGG3w
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.

1.857 Γ— 10⁹⁢(97-digit number)
18575275186736194304…01468908582388999679
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
1.857 Γ— 10⁹⁢(97-digit number)
18575275186736194304…01468908582388999679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.715 Γ— 10⁹⁢(97-digit number)
37150550373472388608…02937817164777999359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.430 Γ— 10⁹⁢(97-digit number)
74301100746944777216…05875634329555998719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.486 Γ— 10⁹⁷(98-digit number)
14860220149388955443…11751268659111997439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.972 Γ— 10⁹⁷(98-digit number)
29720440298777910886…23502537318223994879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.944 Γ— 10⁹⁷(98-digit number)
59440880597555821773…47005074636447989759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.188 Γ— 10⁹⁸(99-digit number)
11888176119511164354…94010149272895979519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.377 Γ— 10⁹⁸(99-digit number)
23776352239022328709…88020298545791959039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.755 Γ— 10⁹⁸(99-digit number)
47552704478044657418…76040597091583918079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.510 Γ— 10⁹⁸(99-digit number)
95105408956089314836…52081194183167836159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.902 Γ— 10⁹⁹(100-digit number)
19021081791217862967…04162388366335672319
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:57,950,100 XPMΒ·at block #6,838,227 Β· updates every 60s
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