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Block #2,649,446

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2018, 6:18:36 AM Β· Difficulty 11.7638 Β· 4,193,646 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e79f4edfd95ff063f8d2f3d535cc4bedbb7d2bb2a23744f8641ce253edebd8c8
View on Chainz β†—

Height

#2,649,446

Difficulty

11.763818

Transactions

1

Size

201 B

Version

2

Bits

0bc38994

Nonce

1,028,238,386

Timestamp

5/5/2018, 6:18:36 AM

Confirmations

4,193,646

Mined by

⛏️ P2SHAGuvzqJ1VWeLpa6eRDAzHZ7zjEj53Rfjob

Merkle Root

225c01398267c84ec5718b165c73e677c282dbd8466c4881b1609d37c881cd76
Transactions (1)
Coinbase225c01398267c8…609d37c881cd76
1 in β†’ 1 out7.2100 XPM110 B
AGuvzqJ1…j53Rfjob
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.

1.255 Γ— 10⁹⁷(98-digit number)
12556618041216792408…89131670014430658561
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
1.255 Γ— 10⁹⁷(98-digit number)
12556618041216792408…89131670014430658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.511 Γ— 10⁹⁷(98-digit number)
25113236082433584816…78263340028861317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.022 Γ— 10⁹⁷(98-digit number)
50226472164867169633…56526680057722634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.004 Γ— 10⁹⁸(99-digit number)
10045294432973433926…13053360115445268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.009 Γ— 10⁹⁸(99-digit number)
20090588865946867853…26106720230890536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.018 Γ— 10⁹⁸(99-digit number)
40181177731893735707…52213440461781073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.036 Γ— 10⁹⁸(99-digit number)
80362355463787471414…04426880923562147841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.607 Γ— 10⁹⁹(100-digit number)
16072471092757494282…08853761847124295681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.214 Γ— 10⁹⁹(100-digit number)
32144942185514988565…17707523694248591361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.428 Γ— 10⁹⁹(100-digit number)
64289884371029977131…35415047388497182721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.285 Γ— 10¹⁰⁰(101-digit number)
12857976874205995426…70830094776994365441
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,989,099 XPMΒ·at block #6,843,091 Β· updates every 60s
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