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Block #2,121,525

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/18/2017, 1:52:24 AM Β· Difficulty 10.9136 Β· 4,709,233 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
93f44e3ded78453f249f56ed228797fee1341cdbe47c6a7e6e10be6bd86b1429
View on Chainz β†—

Height

#2,121,525

Difficulty

10.913595

Transactions

1

Size

208 B

Version

2

Bits

0ae9e15f

Nonce

231,377,094

Timestamp

5/18/2017, 1:52:24 AM

Confirmations

4,709,233

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

c60e1c3ef40d90da5594ca945fc513bd1bf09d1ed323192e56a02a44b2b944f4
Transactions (1)
Coinbasec60e1c3ef40d90…a02a44b2b944f4
1 in β†’ 1 out8.3800 XPM118 B
AM6GYpjw…aw86QDtR
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.

2.448 Γ— 10⁹⁴(95-digit number)
24486461883367589186…34798852094578077079
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
2.448 Γ— 10⁹⁴(95-digit number)
24486461883367589186…34798852094578077079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.897 Γ— 10⁹⁴(95-digit number)
48972923766735178373…69597704189156154159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.794 Γ— 10⁹⁴(95-digit number)
97945847533470356746…39195408378312308319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁡(96-digit number)
19589169506694071349…78390816756624616639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.917 Γ— 10⁹⁡(96-digit number)
39178339013388142698…56781633513249233279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.835 Γ— 10⁹⁡(96-digit number)
78356678026776285396…13563267026498466559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.567 Γ— 10⁹⁢(97-digit number)
15671335605355257079…27126534052996933119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.134 Γ— 10⁹⁢(97-digit number)
31342671210710514158…54253068105993866239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.268 Γ— 10⁹⁢(97-digit number)
62685342421421028317…08506136211987732479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.253 Γ— 10⁹⁷(98-digit number)
12537068484284205663…17012272423975464959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.507 Γ— 10⁹⁷(98-digit number)
25074136968568411327…34024544847950929919
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:57,890,201 XPMΒ·at block #6,830,757 Β· updates every 60s
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