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Block #227,116

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/25/2013, 4:27:30 PM Β· Difficulty 9.9363 Β· 6,583,205 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c3252206f66e4933da7bd2e88180c7716373218135959ec1ef41915d6a0f973b
View on Chainz β†—

Height

#227,116

Difficulty

9.936274

Transactions

1

Size

207 B

Version

2

Bits

09efafa3

Nonce

1,371

Timestamp

10/25/2013, 4:27:30 PM

Confirmations

6,583,205

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

bdff26bf597a15d0e4f6ed6830fc8616ef78d44de28c16c2c0472f9d677fd8d7
Transactions (1)
Coinbasebdff26bf597a15…472f9d677fd8d7
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.042 Γ— 10⁹⁢(97-digit number)
20420443788044282195…41030757448503745919
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
2.042 Γ— 10⁹⁢(97-digit number)
20420443788044282195…41030757448503745919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.084 Γ— 10⁹⁢(97-digit number)
40840887576088564390…82061514897007491839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.168 Γ— 10⁹⁢(97-digit number)
81681775152177128780…64123029794014983679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.633 Γ— 10⁹⁷(98-digit number)
16336355030435425756…28246059588029967359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.267 Γ— 10⁹⁷(98-digit number)
32672710060870851512…56492119176059934719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.534 Γ— 10⁹⁷(98-digit number)
65345420121741703024…12984238352119869439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.306 Γ— 10⁹⁸(99-digit number)
13069084024348340604…25968476704239738879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.613 Γ— 10⁹⁸(99-digit number)
26138168048696681209…51936953408479477759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.227 Γ— 10⁹⁸(99-digit number)
52276336097393362419…03873906816958955519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.045 Γ— 10⁹⁹(100-digit number)
10455267219478672483…07747813633917911039
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:57,726,646 XPMΒ·at block #6,810,320 Β· updates every 60s
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