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Block #2,172,751

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/22/2017, 9:13:30 PM Β· Difficulty 10.9092 Β· 4,671,289 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a2bdbb13fce7403a1893e4adf28ff8f70c052444edebabe978b4d02755b388a4
View on Chainz β†—

Height

#2,172,751

Difficulty

10.909187

Transactions

2

Size

1.86 KB

Version

2

Bits

0ae8c073

Nonce

1,148,474,006

Timestamp

6/22/2017, 9:13:30 PM

Confirmations

4,671,289

Mined by

⛏️ P2SHALsvux9RcGuE6419q3AjA8BPPwLU3Rd6bC

Merkle Root

f9c445485cd66db077502a298c9c499399aa11df22369f64c7d39488be2d8b19
Transactions (2)
Coinbaseee3bdadaaedf6e…8afe9f75ccad00
1 in β†’ 1 out8.4100 XPM110 B
ALsvux9R…LU3Rd6bC
33a6895c4ff7cc…a38abf022a8050
11 in β†’ 2 out0.0900 XPM1.66 KB
ALLBJAEh…3Ws6foW5AGUov8ii…fd8atAoK
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.

1.893 Γ— 10⁹²(93-digit number)
18932577593994075023…75811148533541967479
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
1.893 Γ— 10⁹²(93-digit number)
18932577593994075023…75811148533541967479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.786 Γ— 10⁹²(93-digit number)
37865155187988150046…51622297067083934959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.573 Γ— 10⁹²(93-digit number)
75730310375976300092…03244594134167869919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.514 Γ— 10⁹³(94-digit number)
15146062075195260018…06489188268335739839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.029 Γ— 10⁹³(94-digit number)
30292124150390520036…12978376536671479679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.058 Γ— 10⁹³(94-digit number)
60584248300781040073…25956753073342959359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.211 Γ— 10⁹⁴(95-digit number)
12116849660156208014…51913506146685918719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.423 Γ— 10⁹⁴(95-digit number)
24233699320312416029…03827012293371837439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.846 Γ— 10⁹⁴(95-digit number)
48467398640624832059…07654024586743674879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.693 Γ— 10⁹⁴(95-digit number)
96934797281249664118…15308049173487349759
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:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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