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Block #918,234

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/1/2015, 6:27:09 AM Β· Difficulty 10.9222 Β· 5,888,026 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be8e7775128dde6675fd91ee2daac3ab79a67bea9c3d81c8132b0aedc8ffb599
View on Chainz β†—

Height

#918,234

Difficulty

10.922170

Transactions

2

Size

1.14 KB

Version

2

Bits

0aec1356

Nonce

2,474,298,735

Timestamp

2/1/2015, 6:27:09 AM

Confirmations

5,888,026

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bb26744e0dbdd311462576122a0563cc9e1118e2789d55690d6bf70aed197e3e
Transactions (2)
Coinbasef8b5b4e99666f8…dcca6c134881cf
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
8bcfa4f0cc9628…ebe1f4636bea65
6 in β†’ 2 out315.6886 XPM964 B
APrPrx8n…zGXBhfEcARHxEoP7…Tmn2gL3R
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.

3.702 Γ— 10⁹⁡(96-digit number)
37020550086679812954…02895154876491870559
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
3.702 Γ— 10⁹⁡(96-digit number)
37020550086679812954…02895154876491870559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.404 Γ— 10⁹⁡(96-digit number)
74041100173359625909…05790309752983741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.480 Γ— 10⁹⁢(97-digit number)
14808220034671925181…11580619505967482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.961 Γ— 10⁹⁢(97-digit number)
29616440069343850363…23161239011934964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.923 Γ— 10⁹⁢(97-digit number)
59232880138687700727…46322478023869928959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.184 Γ— 10⁹⁷(98-digit number)
11846576027737540145…92644956047739857919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.369 Γ— 10⁹⁷(98-digit number)
23693152055475080291…85289912095479715839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.738 Γ— 10⁹⁷(98-digit number)
47386304110950160582…70579824190959431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.477 Γ— 10⁹⁷(98-digit number)
94772608221900321164…41159648381918863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.895 Γ— 10⁹⁸(99-digit number)
18954521644380064232…82319296763837726719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,694,164 XPMΒ·at block #6,806,259 Β· updates every 60s
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