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Block #911,858

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/27/2015, 10:52:58 AM Β· Difficulty 10.9301 Β· 5,893,196 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3fbcca4e1612a8958e350d8f8ce3c3d835a46a7248de5fed3a5014ab4156d473
View on Chainz β†—

Height

#911,858

Difficulty

10.930137

Transactions

2

Size

574 B

Version

2

Bits

0aee1d71

Nonce

665,441,447

Timestamp

1/27/2015, 10:52:58 AM

Confirmations

5,893,196

Mined by

⛏️ P2SHAd1Ur2RzLp9MGqJ76yt7A3oiTx1Wvu9BYV

Merkle Root

ff6c04cb22c45df97123099518894d2ec77dd08a680ae0d1b72351bec57ee8a0
Transactions (2)
Coinbase25d4c7203e4d53…46869078b22948
1 in β†’ 1 out8.3700 XPM109 B
Ad1Ur2Rz…1Wvu9BYV
8ac4b5776f4318…0e91414675d432
2 in β†’ 2 out102.7461 XPM376 B
ARoPpPjC…Ndoa3iQvAWXEyvw2…gP7CEjgA
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.

2.185 Γ— 10⁹²(93-digit number)
21853265179223886637…39419317841759147479
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
2.185 Γ— 10⁹²(93-digit number)
21853265179223886637…39419317841759147479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.370 Γ— 10⁹²(93-digit number)
43706530358447773275…78838635683518294959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.741 Γ— 10⁹²(93-digit number)
87413060716895546550…57677271367036589919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.748 Γ— 10⁹³(94-digit number)
17482612143379109310…15354542734073179839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.496 Γ— 10⁹³(94-digit number)
34965224286758218620…30709085468146359679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.993 Γ— 10⁹³(94-digit number)
69930448573516437240…61418170936292719359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.398 Γ— 10⁹⁴(95-digit number)
13986089714703287448…22836341872585438719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.797 Γ— 10⁹⁴(95-digit number)
27972179429406574896…45672683745170877439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.594 Γ— 10⁹⁴(95-digit number)
55944358858813149792…91345367490341754879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁡(96-digit number)
11188871771762629958…82690734980683509759
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:57,684,497 XPMΒ·at block #6,805,053 Β· updates every 60s
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