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Block #2,164,072

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/17/2017, 4:58:15 AM Β· Difficulty 10.8993 Β· 4,652,474 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
167b3bb0f2ffe4fd3f0f823afb1fdedb3273daafb23dd3b8105f3a52a4777b7c
View on Chainz β†—

Height

#2,164,072

Difficulty

10.899331

Transactions

2

Size

5.44 KB

Version

2

Bits

0ae63a8d

Nonce

728,122,540

Timestamp

6/17/2017, 4:58:15 AM

Confirmations

4,652,474

Mined by

⛏️ P2SHAUcDi3vTFKKRLsmDZMZUHn2vZUKoVWoCLx

Merkle Root

c8cd69e8227fd2714b426c96a10e3abdbd22b3fd501ec73ee6c68f9bcf2c2e1d
Transactions (2)
Coinbase223f75df47db39…227fbd2f79849a
1 in β†’ 1 out8.4800 XPM109 B
AUcDi3vT…KoVWoCLx
82a6b9440dca2c…358dbfe28b0e2e
36 in β†’ 1 out1522.2440 XPM5.24 KB
AXNyjfj8…Xjj3ZbFr
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.

2.548 Γ— 10⁹⁢(97-digit number)
25482678528718285844…73324092759557550079
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
2.548 Γ— 10⁹⁢(97-digit number)
25482678528718285844…73324092759557550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.096 Γ— 10⁹⁢(97-digit number)
50965357057436571688…46648185519115100159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.019 Γ— 10⁹⁷(98-digit number)
10193071411487314337…93296371038230200319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.038 Γ— 10⁹⁷(98-digit number)
20386142822974628675…86592742076460400639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.077 Γ— 10⁹⁷(98-digit number)
40772285645949257351…73185484152920801279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.154 Γ— 10⁹⁷(98-digit number)
81544571291898514702…46370968305841602559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.630 Γ— 10⁹⁸(99-digit number)
16308914258379702940…92741936611683205119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.261 Γ— 10⁹⁸(99-digit number)
32617828516759405880…85483873223366410239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.523 Γ— 10⁹⁸(99-digit number)
65235657033518811761…70967746446732820479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.304 Γ— 10⁹⁹(100-digit number)
13047131406703762352…41935492893465640959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.609 Γ— 10⁹⁹(100-digit number)
26094262813407524704…83870985786931281919
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:57,776,497 XPMΒ·at block #6,816,545 Β· updates every 60s
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