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Block #2,287,209

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2017, 2:26:42 AM Β· Difficulty 10.9555 Β· 4,528,757 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3152b5234165ff7871791ace4af26eef666fdf6c20dece3ca493c31366970d5f
View on Chainz β†—

Height

#2,287,209

Difficulty

10.955549

Transactions

2

Size

425 B

Version

2

Bits

0af49ed4

Nonce

1,967,981,219

Timestamp

9/8/2017, 2:26:42 AM

Confirmations

4,528,757

Mined by

⛏️ P2SHAJqkZ5AYNtLXDsa67GpSYVoHoX7gCPfbpN

Merkle Root

2d2f1d894121fefb0b16c15be30e8891b1cbc4c4628f091c2019496b6b01ad99
Transactions (2)
Coinbase40995e9cbd327a…390453af14a371
1 in β†’ 1 out8.3300 XPM109 B
AJqkZ5AY…7gCPfbpN
af9662d42c0275…35d271bc38ea92
1 in β†’ 2 out2300.6408 XPM226 B
AYq6rfSR…Keo6SMonAVmoJz1r…1YfwF8HS
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.

1.016 Γ— 10⁹⁡(96-digit number)
10163104355916213373…73271493617282365439
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
1.016 Γ— 10⁹⁡(96-digit number)
10163104355916213373…73271493617282365439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.032 Γ— 10⁹⁡(96-digit number)
20326208711832426747…46542987234564730879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.065 Γ— 10⁹⁡(96-digit number)
40652417423664853494…93085974469129461759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.130 Γ— 10⁹⁡(96-digit number)
81304834847329706988…86171948938258923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.626 Γ— 10⁹⁢(97-digit number)
16260966969465941397…72343897876517847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.252 Γ— 10⁹⁢(97-digit number)
32521933938931882795…44687795753035694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.504 Γ— 10⁹⁢(97-digit number)
65043867877863765590…89375591506071388159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.300 Γ— 10⁹⁷(98-digit number)
13008773575572753118…78751183012142776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.601 Γ— 10⁹⁷(98-digit number)
26017547151145506236…57502366024285552639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.203 Γ— 10⁹⁷(98-digit number)
52035094302291012472…15004732048571105279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,771,840 XPMΒ·at block #6,815,965 Β· updates every 60s
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