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Block #2,280,278

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/3/2017, 5:26:03 AM Β· Difficulty 10.9561 Β· 4,556,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65247ef22fb8e250d8c0b037760891a79e6bf35478f4e8d1149d998e285ed626
View on Chainz β†—

Height

#2,280,278

Difficulty

10.956132

Transactions

2

Size

30.00 KB

Version

2

Bits

0af4c50e

Nonce

528,092,776

Timestamp

9/3/2017, 5:26:03 AM

Confirmations

4,556,075

Mined by

⛏️ P2SHAVYmpeugRv1CxWoJubDxQduoLPL6odyVVh

Merkle Root

4bfb8bd36d5fc63d5ed61fa7cc9f724d40961249ab8271b949a48e301b289813
Transactions (2)
Coinbaseb2b446433e5400…ed889770dc69fb
1 in β†’ 1 out8.6300 XPM110 B
AVYmpeug…L6odyVVh
46eae91e7503c0…a81800e350fc26
206 in β†’ 1 out77442.6533 XPM29.80 KB
ARQv2vg4…TAfitw4u
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.

5.323 Γ— 10⁹⁡(96-digit number)
53238028244826019204…20528159855196671999
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
5.323 Γ— 10⁹⁡(96-digit number)
53238028244826019204…20528159855196671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.064 Γ— 10⁹⁢(97-digit number)
10647605648965203840…41056319710393343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.129 Γ— 10⁹⁢(97-digit number)
21295211297930407681…82112639420786687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.259 Γ— 10⁹⁢(97-digit number)
42590422595860815363…64225278841573375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.518 Γ— 10⁹⁢(97-digit number)
85180845191721630727…28450557683146751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.703 Γ— 10⁹⁷(98-digit number)
17036169038344326145…56901115366293503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.407 Γ— 10⁹⁷(98-digit number)
34072338076688652290…13802230732587007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.814 Γ— 10⁹⁷(98-digit number)
68144676153377304581…27604461465174015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.362 Γ— 10⁹⁸(99-digit number)
13628935230675460916…55208922930348031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.725 Γ— 10⁹⁸(99-digit number)
27257870461350921832…10417845860696063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.451 Γ— 10⁹⁸(99-digit number)
54515740922701843665…20835691721392127999
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:57,935,084 XPMΒ·at block #6,836,352 Β· updates every 60s
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