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Block #2,237,882

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2017, 9:50:37 AM Β· Difficulty 10.9461 Β· 4,600,352 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c6d56d8903344c5fca5e6a6c659846ff2f30f07348db7ac0dbea0a5bbbb2c91f
View on Chainz β†—

Height

#2,237,882

Difficulty

10.946147

Transactions

2

Size

1.28 KB

Version

2

Bits

0af236b3

Nonce

192,197,320

Timestamp

8/5/2017, 9:50:37 AM

Confirmations

4,600,352

Mined by

⛏️ P2SHAdSDjYryhERrh1uGy3Szga2PDMEsvu5EVD

Merkle Root

7b4adf78d64489b48a4e2a64df9d3a99ef9d727351bda7b05fd6caa9aedaf76e
Transactions (2)
Coinbaseea56d36d518902…4b39dee8c4f80b
1 in β†’ 1 out8.3500 XPM110 B
AdSDjYry…Esvu5EVD
937fac50925990…49fc6d02919c02
7 in β†’ 2 out1096.9205 XPM1.09 KB
ARLxMe9N…Bxx8GE18AV2JtV8F…uQ3r1jRg
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.

2.914 Γ— 10⁹⁴(95-digit number)
29148538804375042133…95139081664434697919
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
2.914 Γ— 10⁹⁴(95-digit number)
29148538804375042133…95139081664434697919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.829 Γ— 10⁹⁴(95-digit number)
58297077608750084267…90278163328869395839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.165 Γ— 10⁹⁡(96-digit number)
11659415521750016853…80556326657738791679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.331 Γ— 10⁹⁡(96-digit number)
23318831043500033707…61112653315477583359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.663 Γ— 10⁹⁡(96-digit number)
46637662087000067414…22225306630955166719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.327 Γ— 10⁹⁡(96-digit number)
93275324174000134828…44450613261910333439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁢(97-digit number)
18655064834800026965…88901226523820666879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.731 Γ— 10⁹⁢(97-digit number)
37310129669600053931…77802453047641333759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.462 Γ— 10⁹⁢(97-digit number)
74620259339200107862…55604906095282667519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁷(98-digit number)
14924051867840021572…11209812190565335039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁷(98-digit number)
29848103735680043145…22419624381130670079
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:57,950,147 XPMΒ·at block #6,838,233 Β· updates every 60s
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