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Block #2,825,434

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2018, 6:29:48 AM Β· Difficulty 11.7092 Β· 4,006,324 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0fceee30ec85b96013bb5feb2fb4bec708e8ffbc3a693d7e4d5a6697a88a2255
View on Chainz β†—

Height

#2,825,434

Difficulty

11.709214

Transactions

2

Size

573 B

Version

2

Bits

0bb58f0d

Nonce

2,111,781,245

Timestamp

9/5/2018, 6:29:48 AM

Confirmations

4,006,324

Mined by

⛏️ P2SHAekoZgRDRnNTNSeSaDX6Cg7tGDtVdAtqAr

Merkle Root

3485e8edec4a4c87ee732322d82bf7156c666e352de6bcc9f6253cd3bcacaaf1
Transactions (2)
Coinbasebe23dcb2f241f1…a38f49cdda5043
1 in β†’ 1 out7.3000 XPM109 B
AekoZgRD…tVdAtqAr
886d3dd605d00f…482d63922c7739
2 in β†’ 2 out100.4442 XPM374 B
Aec2BYT7…i7ZdvzckANKw3Z5i…Qp2MZ4wE
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.

1.044 Γ— 10⁹⁴(95-digit number)
10445739186359694867…13418122910560300399
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
1.044 Γ— 10⁹⁴(95-digit number)
10445739186359694867…13418122910560300399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.089 Γ— 10⁹⁴(95-digit number)
20891478372719389735…26836245821120600799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.178 Γ— 10⁹⁴(95-digit number)
41782956745438779471…53672491642241201599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.356 Γ— 10⁹⁴(95-digit number)
83565913490877558943…07344983284482403199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.671 Γ— 10⁹⁡(96-digit number)
16713182698175511788…14689966568964806399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.342 Γ— 10⁹⁡(96-digit number)
33426365396351023577…29379933137929612799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.685 Γ— 10⁹⁡(96-digit number)
66852730792702047154…58759866275859225599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.337 Γ— 10⁹⁢(97-digit number)
13370546158540409430…17519732551718451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.674 Γ— 10⁹⁢(97-digit number)
26741092317080818861…35039465103436902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.348 Γ— 10⁹⁢(97-digit number)
53482184634161637723…70078930206873804799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁷(98-digit number)
10696436926832327544…40157860413747609599
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:57,898,173 XPMΒ·at block #6,831,757 Β· updates every 60s
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