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Block #2,640,244

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 10:34:44 PM Β· Difficulty 11.5731 Β· 4,197,538 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c34da9529cc956a048bdbae4a209118514ab29fd5ede07bb4e4edbdce7de3ff5
View on Chainz β†—

Height

#2,640,244

Difficulty

11.573102

Transactions

1

Size

200 B

Version

2

Bits

0b92b6cd

Nonce

133,798,870

Timestamp

4/30/2018, 10:34:44 PM

Confirmations

4,197,538

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

f306e26e610470f864e8c730d29597255e8fa478011e1b1ea87c9a3865f50d25
Transactions (1)
Coinbasef306e26e610470…7c9a3865f50d25
1 in β†’ 1 out7.4500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.533 Γ— 10⁹⁡(96-digit number)
15339924396267195191…74151644264542425599
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
1.533 Γ— 10⁹⁡(96-digit number)
15339924396267195191…74151644264542425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.067 Γ— 10⁹⁡(96-digit number)
30679848792534390382…48303288529084851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.135 Γ— 10⁹⁡(96-digit number)
61359697585068780765…96606577058169702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁢(97-digit number)
12271939517013756153…93213154116339404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁢(97-digit number)
24543879034027512306…86426308232678809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.908 Γ— 10⁹⁢(97-digit number)
49087758068055024612…72852616465357619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.817 Γ— 10⁹⁢(97-digit number)
98175516136110049225…45705232930715238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.963 Γ— 10⁹⁷(98-digit number)
19635103227222009845…91410465861430476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.927 Γ— 10⁹⁷(98-digit number)
39270206454444019690…82820931722860953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.854 Γ— 10⁹⁷(98-digit number)
78540412908888039380…65641863445721907199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.570 Γ— 10⁹⁸(99-digit number)
15708082581777607876…31283726891443814399
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:57,946,593 XPMΒ·at block #6,837,781 Β· updates every 60s
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