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Block #2,628,541

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/25/2018, 1:05:12 AM Β· Difficulty 11.1920 Β· 4,203,094 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31b3ddc3d27aca3a22ad3b78345d6bca5bb67b4ec62daf8792e9c085463c35b4
View on Chainz β†—

Height

#2,628,541

Difficulty

11.192002

Transactions

2

Size

65.59 KB

Version

2

Bits

0b312712

Nonce

2,122,527,362

Timestamp

4/25/2018, 1:05:12 AM

Confirmations

4,203,094

Mined by

⛏️ P2SHAWMnrrXvhAg8RpQGUsTq6tMgKuC3NAzjD4

Merkle Root

6c677a15b502204aeb6b0f27d2219bf6d1bc2c4d659753d8a27d3501d44fd650
Transactions (2)
Coinbase60f09051bbb4ed…1487cccbe81cb3
1 in β†’ 1 out8.6600 XPM110 B
AWMnrrXv…C3NAzjD4
da461938a72e07…574e602f008e9b
452 in β†’ 2 out3942.2293 XPM65.40 KB
AXTBX7BZ…Zn6VCbzqAXDznZG3…PDHnfomC
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.

6.026 Γ— 10⁹³(94-digit number)
60265520053911310804…48553661813186217679
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
6.026 Γ— 10⁹³(94-digit number)
60265520053911310804…48553661813186217679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁴(95-digit number)
12053104010782262160…97107323626372435359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.410 Γ— 10⁹⁴(95-digit number)
24106208021564524321…94214647252744870719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.821 Γ— 10⁹⁴(95-digit number)
48212416043129048643…88429294505489741439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.642 Γ— 10⁹⁴(95-digit number)
96424832086258097286…76858589010979482879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.928 Γ— 10⁹⁡(96-digit number)
19284966417251619457…53717178021958965759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.856 Γ— 10⁹⁡(96-digit number)
38569932834503238914…07434356043917931519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.713 Γ— 10⁹⁡(96-digit number)
77139865669006477829…14868712087835863039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.542 Γ— 10⁹⁢(97-digit number)
15427973133801295565…29737424175671726079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.085 Γ— 10⁹⁢(97-digit number)
30855946267602591131…59474848351343452159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.171 Γ— 10⁹⁢(97-digit number)
61711892535205182263…18949696702686904319
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:57,897,183 XPMΒ·at block #6,831,634 Β· updates every 60s
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