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Block #2,647,615

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 12:46:24 AM Β· Difficulty 11.7610 Β· 4,178,499 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e610fc9a56f8ca86a13bab22382b665776136edd2d01633f2632deea22502772
View on Chainz β†—

Height

#2,647,615

Difficulty

11.761007

Transactions

2

Size

65.54 KB

Version

2

Bits

0bc2d163

Nonce

208,628,198

Timestamp

5/4/2018, 12:46:24 AM

Confirmations

4,178,499

Mined by

⛏️ P2SHAX48nzZZuQ5wNg4Xq6tPfn9cBzQj29Qgcv

Merkle Root

68a03c124227c79a366a5ba487530216e642ecebb7b07cb95d658df190502ecd
Transactions (2)
Coinbasec4f546e93b92ee…8929da929c18e4
1 in β†’ 1 out7.8900 XPM110 B
AX48nzZZ…Qj29Qgcv
0261c739226ff2…9a5a4ee16ababf
452 in β†’ 1 out17017.3438 XPM65.35 KB
ALPF8J52…Hjw4BMsG
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.

6.572 Γ— 10⁹⁢(97-digit number)
65728341946096336769…45761896914347038719
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
6.572 Γ— 10⁹⁢(97-digit number)
65728341946096336769…45761896914347038719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.314 Γ— 10⁹⁷(98-digit number)
13145668389219267353…91523793828694077439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.629 Γ— 10⁹⁷(98-digit number)
26291336778438534707…83047587657388154879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.258 Γ— 10⁹⁷(98-digit number)
52582673556877069415…66095175314776309759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.051 Γ— 10⁹⁸(99-digit number)
10516534711375413883…32190350629552619519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.103 Γ— 10⁹⁸(99-digit number)
21033069422750827766…64380701259105239039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.206 Γ— 10⁹⁸(99-digit number)
42066138845501655532…28761402518210478079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.413 Γ— 10⁹⁸(99-digit number)
84132277691003311065…57522805036420956159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.682 Γ— 10⁹⁹(100-digit number)
16826455538200662213…15045610072841912319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.365 Γ— 10⁹⁹(100-digit number)
33652911076401324426…30091220145683824639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.730 Γ— 10⁹⁹(100-digit number)
67305822152802648852…60182440291367649279
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:57,853,037 XPMΒ·at block #6,826,113 Β· updates every 60s
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