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Block #2,877,525

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/12/2018, 3:06:16 AM Β· Difficulty 11.6484 Β· 3,964,936 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2d2672179abc71d955ea84cbede46bdda9d24bb41bab09c45a1e399b71811961
View on Chainz β†—

Height

#2,877,525

Difficulty

11.648423

Transactions

1

Size

201 B

Version

2

Bits

0ba5ff13

Nonce

475,414,195

Timestamp

10/12/2018, 3:06:16 AM

Confirmations

3,964,936

Mined by

⛏️ P2SHAbj5r7t5MZWbRk9eyVDbxGC5uv7dTFbfbu

Merkle Root

bbe4cbfda21997b6c3f040a83ff90b2706cd5190ef71b64b1a0b5d3910771853
Transactions (1)
Coinbasebbe4cbfda21997…0b5d3910771853
1 in β†’ 1 out7.3600 XPM110 B
Abj5r7t5…7dTFbfbu
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.

1.017 Γ— 10⁹⁢(97-digit number)
10172308336652836419…95720280391920075679
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
1.017 Γ— 10⁹⁢(97-digit number)
10172308336652836419…95720280391920075679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.034 Γ— 10⁹⁢(97-digit number)
20344616673305672838…91440560783840151359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.068 Γ— 10⁹⁢(97-digit number)
40689233346611345677…82881121567680302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.137 Γ— 10⁹⁢(97-digit number)
81378466693222691354…65762243135360605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.627 Γ— 10⁹⁷(98-digit number)
16275693338644538270…31524486270721210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.255 Γ— 10⁹⁷(98-digit number)
32551386677289076541…63048972541442421759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.510 Γ— 10⁹⁷(98-digit number)
65102773354578153083…26097945082884843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁸(99-digit number)
13020554670915630616…52195890165769687039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.604 Γ— 10⁹⁸(99-digit number)
26041109341831261233…04391780331539374079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.208 Γ— 10⁹⁸(99-digit number)
52082218683662522466…08783560663078748159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁹(100-digit number)
10416443736732504493…17567121326157496319
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:57,984,105 XPMΒ·at block #6,842,460 Β· updates every 60s
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