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Block #2,106,586

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/8/2017, 12:25:57 PM Β· Difficulty 10.8904 Β· 4,710,339 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91f35359dca286460a17261a0979937d2f63b696a87aa4ace9b4485237702f40
View on Chainz β†—

Height

#2,106,586

Difficulty

10.890428

Transactions

2

Size

15.86 KB

Version

2

Bits

0ae3f319

Nonce

934,443,048

Timestamp

5/8/2017, 12:25:57 PM

Confirmations

4,710,339

Mined by

⛏️ P2SHAZz5jAFXenBa9H6mjc5Q8EfjotddE2wKZX

Merkle Root

b7bd89195813b140cc66a47586451ebcb56f359dc27f0d79d1dfbc01fac17992
Transactions (2)
Coinbase16dda12557d6e5…f192942b5dd281
1 in β†’ 1 out9.1500 XPM110 B
AZz5jAFX…ddE2wKZX
a3f71b36c1b54f…e74c8237c8b66c
108 in β†’ 1 out4.4917 XPM15.67 KB
AKGxoSP8…8oH3hVLd
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.

9.507 Γ— 10⁹⁡(96-digit number)
95075015198423324355…11689660144160220159
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
9.507 Γ— 10⁹⁡(96-digit number)
95075015198423324355…11689660144160220159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.901 Γ— 10⁹⁢(97-digit number)
19015003039684664871…23379320288320440319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.803 Γ— 10⁹⁢(97-digit number)
38030006079369329742…46758640576640880639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.606 Γ— 10⁹⁢(97-digit number)
76060012158738659484…93517281153281761279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.521 Γ— 10⁹⁷(98-digit number)
15212002431747731896…87034562306563522559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.042 Γ— 10⁹⁷(98-digit number)
30424004863495463793…74069124613127045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.084 Γ— 10⁹⁷(98-digit number)
60848009726990927587…48138249226254090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.216 Γ— 10⁹⁸(99-digit number)
12169601945398185517…96276498452508180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.433 Γ— 10⁹⁸(99-digit number)
24339203890796371035…92552996905016360959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.867 Γ— 10⁹⁸(99-digit number)
48678407781592742070…85105993810032721919
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:57,779,441 XPMΒ·at block #6,816,924 Β· updates every 60s
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