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Block #2,637,998

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 3:13:41 AM Β· Difficulty 11.4704 Β· 4,205,351 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8fb67d2517903f4ba7c595255a1742c0dc08b9c0a7c109f4b8a9118dd11254c4
View on Chainz β†—

Height

#2,637,998

Difficulty

11.470446

Transactions

1

Size

201 B

Version

2

Bits

0b786f1f

Nonce

337,984,212

Timestamp

4/30/2018, 3:13:41 AM

Confirmations

4,205,351

Mined by

⛏️ P2SHAZ5t1WrG4ndRRjF45uidtn5of9zo3YcwXx

Merkle Root

6d1f72c76e56bcb1cca29aecaced3b828a9cc72b8be1909d9d6fd83aaeab88da
Transactions (1)
Coinbase6d1f72c76e56bc…6fd83aaeab88da
1 in β†’ 1 out7.5900 XPM110 B
AZ5t1WrG…zo3YcwXx
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.

7.588 Γ— 10⁹⁢(97-digit number)
75887797194956666773…48129414727895183359
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
7.588 Γ— 10⁹⁢(97-digit number)
75887797194956666773…48129414727895183359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.517 Γ— 10⁹⁷(98-digit number)
15177559438991333354…96258829455790366719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.035 Γ— 10⁹⁷(98-digit number)
30355118877982666709…92517658911580733439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.071 Γ— 10⁹⁷(98-digit number)
60710237755965333418…85035317823161466879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.214 Γ— 10⁹⁸(99-digit number)
12142047551193066683…70070635646322933759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.428 Γ— 10⁹⁸(99-digit number)
24284095102386133367…40141271292645867519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.856 Γ— 10⁹⁸(99-digit number)
48568190204772266735…80282542585291735039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.713 Γ— 10⁹⁸(99-digit number)
97136380409544533470…60565085170583470079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.942 Γ— 10⁹⁹(100-digit number)
19427276081908906694…21130170341166940159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.885 Γ— 10⁹⁹(100-digit number)
38854552163817813388…42260340682333880319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.770 Γ— 10⁹⁹(100-digit number)
77709104327635626776…84520681364667760639
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:57,991,153 XPMΒ·at block #6,843,348 Β· updates every 60s
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