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Block #2,270,332

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2017, 1:16:59 PM Β· Difficulty 10.9528 Β· 4,569,276 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e3c7f6d527c8b0f09fdbe61e6fd5caf32bb3e7ecae9b546c238fcf447bb5ac6
View on Chainz β†—

Height

#2,270,332

Difficulty

10.952768

Transactions

1

Size

200 B

Version

2

Bits

0af3e89e

Nonce

87,574,310

Timestamp

8/27/2017, 1:16:59 PM

Confirmations

4,569,276

Mined by

⛏️ P2SHAb7acy4taLLcaEFU5y7GWYWYzRxoQpWMr9

Merkle Root

46465b38547c02ed70b149ef8ceb5b6616ff4326d8e956ff5590ed960b2f0948
Transactions (1)
Coinbase46465b38547c02…90ed960b2f0948
1 in β†’ 1 out8.3200 XPM110 B
Ab7acy4t…xoQpWMr9
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.

2.442 Γ— 10⁹⁡(96-digit number)
24428504156740523285…13785508690127431679
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
2.442 Γ— 10⁹⁡(96-digit number)
24428504156740523285…13785508690127431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.885 Γ— 10⁹⁡(96-digit number)
48857008313481046571…27571017380254863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.771 Γ— 10⁹⁡(96-digit number)
97714016626962093143…55142034760509726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.954 Γ— 10⁹⁢(97-digit number)
19542803325392418628…10284069521019453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.908 Γ— 10⁹⁢(97-digit number)
39085606650784837257…20568139042038906879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.817 Γ— 10⁹⁢(97-digit number)
78171213301569674514…41136278084077813759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.563 Γ— 10⁹⁷(98-digit number)
15634242660313934902…82272556168155627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.126 Γ— 10⁹⁷(98-digit number)
31268485320627869805…64545112336311255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.253 Γ— 10⁹⁷(98-digit number)
62536970641255739611…29090224672622510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁸(99-digit number)
12507394128251147922…58180449345245020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.501 Γ— 10⁹⁸(99-digit number)
25014788256502295844…16360898690490040319
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:57,961,153 XPMΒ·at block #6,839,607 Β· updates every 60s
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