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Block #2,119,853

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/16/2017, 11:50:24 PM Β· Difficulty 10.9116 Β· 4,711,905 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1f4f2c3595ee0e4e362aa128c3a19bf3d5a136e966cf0a3f4de87380fc1f14c
View on Chainz β†—

Height

#2,119,853

Difficulty

10.911634

Transactions

1

Size

209 B

Version

2

Bits

0ae960d3

Nonce

411,542,972

Timestamp

5/16/2017, 11:50:24 PM

Confirmations

4,711,905

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

bc11f0ae355dbe734c5d48492a24478cc7bfd42be680e03399b7429b54c35a47
Transactions (1)
Coinbasebc11f0ae355dbe…b7429b54c35a47
1 in β†’ 1 out8.3900 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.

3.625 Γ— 10⁹⁢(97-digit number)
36255722626035738813…55020066027218693119
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
3.625 Γ— 10⁹⁢(97-digit number)
36255722626035738813…55020066027218693119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.251 Γ— 10⁹⁢(97-digit number)
72511445252071477626…10040132054437386239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.450 Γ— 10⁹⁷(98-digit number)
14502289050414295525…20080264108874772479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.900 Γ— 10⁹⁷(98-digit number)
29004578100828591050…40160528217749544959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.800 Γ— 10⁹⁷(98-digit number)
58009156201657182101…80321056435499089919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.160 Γ— 10⁹⁸(99-digit number)
11601831240331436420…60642112870998179839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.320 Γ— 10⁹⁸(99-digit number)
23203662480662872840…21284225741996359679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.640 Γ— 10⁹⁸(99-digit number)
46407324961325745681…42568451483992719359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.281 Γ— 10⁹⁸(99-digit number)
92814649922651491362…85136902967985438719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁹(100-digit number)
18562929984530298272…70273805935970877439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.712 Γ— 10⁹⁹(100-digit number)
37125859969060596544…40547611871941754879
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:57,898,173 XPMΒ·at block #6,831,757 Β· updates every 60s
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