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Block #40,529

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 3:09:37 PM Β· Difficulty 8.4406 Β· 6,761,696 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c85463a3470c884a8f32538d462ced01dc306de75dd4a4ddb5e952e6f676d634
View on Chainz β†—

Height

#40,529

Difficulty

8.440591

Transactions

2

Size

1.58 KB

Version

2

Bits

0870ca8d

Nonce

1,557

Timestamp

7/14/2013, 3:09:37 PM

Confirmations

6,761,696

Mined by

⛏️ P2SHANdP9yHd2CL7bMS42oa4VKYcGqs5j8aMNm

Merkle Root

3fcaa3ec1a95eca8a835c572a2dde4249a75452dda9819e1be31a0c8d4645113
Transactions (2)
Coinbasee7669b47a1fd36…3a42d419b253c7
1 in β†’ 1 out14.0400 XPM109 B
ANdP9yHd…s5j8aMNm
3905ddbedf2c9c…36c198d5d5acb1
12 in β†’ 1 out200.0000 XPM1.38 KB
AWSv6hg4…QvGk9TGY
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.

3.124 Γ— 10⁹⁢(97-digit number)
31243328933986240095…67193939076816612349
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
3.124 Γ— 10⁹⁢(97-digit number)
31243328933986240095…67193939076816612349
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.248 Γ— 10⁹⁢(97-digit number)
62486657867972480190…34387878153633224699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.249 Γ— 10⁹⁷(98-digit number)
12497331573594496038…68775756307266449399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.499 Γ— 10⁹⁷(98-digit number)
24994663147188992076…37551512614532898799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.998 Γ— 10⁹⁷(98-digit number)
49989326294377984152…75103025229065797599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.997 Γ— 10⁹⁷(98-digit number)
99978652588755968305…50206050458131595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.999 Γ— 10⁹⁸(99-digit number)
19995730517751193661…00412100916263190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.999 Γ— 10⁹⁸(99-digit number)
39991461035502387322…00824201832526380799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,661,806 XPMΒ·at block #6,802,224 Β· updates every 60s
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