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Block #4,104,198

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2021, 12:20:10 PM Β· Difficulty 10.8084 Β· 2,701,897 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d67945f7d97588071c87d3cb937eec4e657eee5b92df6967646bf6eb39761860
View on Chainz β†—

Height

#4,104,198

Difficulty

10.808403

Transactions

1

Size

199 B

Version

2

Bits

0acef382

Nonce

1,422,923,671

Timestamp

3/3/2021, 12:20:10 PM

Confirmations

2,701,897

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMzVisit pool β†—

Merkle Root

6d638b3b6e889567029ea9b2f414bb1ff20464d1f49c8df3678a681cd8864393
Transactions (1)
Coinbase6d638b3b6e8895…8a681cd8864393
1 in β†’ 1 out8.5500 XPM109 B
AXfJqzUb…HXeXmjMz
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.

3.177 Γ— 10⁹⁴(95-digit number)
31778759461858278722…66987082839992604641
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.177 Γ— 10⁹⁴(95-digit number)
31778759461858278722…66987082839992604641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.355 Γ— 10⁹⁴(95-digit number)
63557518923716557444…33974165679985209281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.271 Γ— 10⁹⁡(96-digit number)
12711503784743311488…67948331359970418561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.542 Γ— 10⁹⁡(96-digit number)
25423007569486622977…35896662719940837121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.084 Γ— 10⁹⁡(96-digit number)
50846015138973245955…71793325439881674241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.016 Γ— 10⁹⁢(97-digit number)
10169203027794649191…43586650879763348481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.033 Γ— 10⁹⁢(97-digit number)
20338406055589298382…87173301759526696961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.067 Γ— 10⁹⁢(97-digit number)
40676812111178596764…74346603519053393921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.135 Γ— 10⁹⁢(97-digit number)
81353624222357193528…48693207038106787841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.627 Γ— 10⁹⁷(98-digit number)
16270724844471438705…97386414076213575681
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,692,833 XPMΒ·at block #6,806,094 Β· updates every 60s
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