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Block #2,111,133

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/11/2017, 5:39:17 AM Β· Difficulty 10.9035 Β· 4,730,651 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c93e7d6a1513992b960a1912bca5a6b3ca4a047baa7c19ebfb3be970e8318945
View on Chainz β†—

Height

#2,111,133

Difficulty

10.903522

Transactions

1

Size

199 B

Version

2

Bits

0ae74d3c

Nonce

1,416,871,209

Timestamp

5/11/2017, 5:39:17 AM

Confirmations

4,730,651

Mined by

⛏️ P2SHAURAmLdLfE5HXED1srgGJepEaVq4nZui2N

Merkle Root

930dce4ab0cba1cb3cbc2e1805a3b57324de08eaccbb68febb251273d50cb617
Transactions (1)
Coinbase930dce4ab0cba1…251273d50cb617
1 in β†’ 1 out8.4000 XPM109 B
AURAmLdL…q4nZui2N
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.

6.365 Γ— 10⁹⁴(95-digit number)
63651183375268716663…58353917821748545439
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
6.365 Γ— 10⁹⁴(95-digit number)
63651183375268716663…58353917821748545439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.273 Γ— 10⁹⁡(96-digit number)
12730236675053743332…16707835643497090879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.546 Γ— 10⁹⁡(96-digit number)
25460473350107486665…33415671286994181759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.092 Γ— 10⁹⁡(96-digit number)
50920946700214973330…66831342573988363519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.018 Γ— 10⁹⁢(97-digit number)
10184189340042994666…33662685147976727039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.036 Γ— 10⁹⁢(97-digit number)
20368378680085989332…67325370295953454079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.073 Γ— 10⁹⁢(97-digit number)
40736757360171978664…34650740591906908159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.147 Γ— 10⁹⁢(97-digit number)
81473514720343957328…69301481183813816319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.629 Γ— 10⁹⁷(98-digit number)
16294702944068791465…38602962367627632639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.258 Γ— 10⁹⁷(98-digit number)
32589405888137582931…77205924735255265279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.517 Γ— 10⁹⁷(98-digit number)
65178811776275165863…54411849470510530559
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:57,978,649 XPMΒ·at block #6,841,783 Β· updates every 60s
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