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Block #2,825,503

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2018, 7:27:12 AM Β· Difficulty 11.7098 Β· 4,012,792 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fa5731dc0be067262c4576467b2e4fd6b6e843b39bbb61b8d8474779d0cddec9
View on Chainz β†—

Height

#2,825,503

Difficulty

11.709760

Transactions

1

Size

200 B

Version

2

Bits

0bb5b2d8

Nonce

299,848,227

Timestamp

9/5/2018, 7:27:12 AM

Confirmations

4,012,792

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

73f1049fff0884164112023fda036a4355342ca75a16dbf879ae1fe0135fbb57
Transactions (1)
Coinbase73f1049fff0884…ae1fe0135fbb57
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.716 Γ— 10⁹⁴(95-digit number)
27161932441261577690…60517948599817688959
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
2.716 Γ— 10⁹⁴(95-digit number)
27161932441261577690…60517948599817688959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.432 Γ— 10⁹⁴(95-digit number)
54323864882523155381…21035897199635377919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.086 Γ— 10⁹⁡(96-digit number)
10864772976504631076…42071794399270755839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.172 Γ— 10⁹⁡(96-digit number)
21729545953009262152…84143588798541511679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.345 Γ— 10⁹⁡(96-digit number)
43459091906018524305…68287177597083023359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.691 Γ— 10⁹⁡(96-digit number)
86918183812037048611…36574355194166046719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.738 Γ— 10⁹⁢(97-digit number)
17383636762407409722…73148710388332093439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.476 Γ— 10⁹⁢(97-digit number)
34767273524814819444…46297420776664186879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.953 Γ— 10⁹⁢(97-digit number)
69534547049629638888…92594841553328373759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.390 Γ— 10⁹⁷(98-digit number)
13906909409925927777…85189683106656747519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.781 Γ— 10⁹⁷(98-digit number)
27813818819851855555…70379366213313495039
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
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