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Block #2,832,953

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 10:07:36 AM Β· Difficulty 11.7151 Β· 4,007,459 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0146bd5c8e352986e694ef87cc9ceb222d34dcca2984a33b06603f82c1001124
View on Chainz β†—

Height

#2,832,953

Difficulty

11.715092

Transactions

1

Size

200 B

Version

2

Bits

0bb71044

Nonce

822,732,809

Timestamp

9/10/2018, 10:07:36 AM

Confirmations

4,007,459

Mined by

⛏️ P2SHAXra7S9wDz4jPYH65vJ1URHUhXi5XZsiZy

Merkle Root

fa08b4ce345a2e6d09afdd10ed150ace29a3c1c9633039ce5fa0288d6c5699a3
Transactions (1)
Coinbasefa08b4ce345a2e…a0288d6c5699a3
1 in β†’ 1 out7.2700 XPM110 B
AXra7S9w…i5XZsiZy
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.

4.080 Γ— 10⁹³(94-digit number)
40806955879623348172…02215939244592227249
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
4.080 Γ— 10⁹³(94-digit number)
40806955879623348172…02215939244592227249
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.161 Γ— 10⁹³(94-digit number)
81613911759246696345…04431878489184454499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.632 Γ— 10⁹⁴(95-digit number)
16322782351849339269…08863756978368908999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.264 Γ— 10⁹⁴(95-digit number)
32645564703698678538…17727513956737817999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.529 Γ— 10⁹⁴(95-digit number)
65291129407397357076…35455027913475635999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁡(96-digit number)
13058225881479471415…70910055826951271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.611 Γ— 10⁹⁡(96-digit number)
26116451762958942830…41820111653902543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.223 Γ— 10⁹⁡(96-digit number)
52232903525917885661…83640223307805087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁢(97-digit number)
10446580705183577132…67280446615610175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.089 Γ— 10⁹⁢(97-digit number)
20893161410367154264…34560893231220351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.178 Γ— 10⁹⁢(97-digit number)
41786322820734308529…69121786462440703999
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:57,967,620 XPMΒ·at block #6,840,411 Β· updates every 60s
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