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Block #1,099,178

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/10/2015, 11:31:57 PM Β· Difficulty 10.7618 Β· 5,715,036 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b5dc8272a824872d5201cd39d5a155ebc40506153a69242ce016f23e84e67d67
View on Chainz β†—

Height

#1,099,178

Difficulty

10.761844

Transactions

1

Size

199 B

Version

2

Bits

0ac3083b

Nonce

269,374

Timestamp

6/10/2015, 11:31:57 PM

Confirmations

5,715,036

Mined by

⛏️ P2SHARaPyHgjo2zpePAfC2xk8aeQGMnA9veLYH

Merkle Root

91a7891d2652080ad0003bb84ffb1d4454a43006af8c04bd8655c5f4a318056a
Transactions (1)
Coinbase91a7891d265208…55c5f4a318056a
1 in β†’ 1 out8.6200 XPM109 B
ARaPyHgj…nA9veLYH
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.

1.070 Γ— 10⁹⁴(95-digit number)
10704165843463591401…44869180303814710399
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
1.070 Γ— 10⁹⁴(95-digit number)
10704165843463591401…44869180303814710399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.140 Γ— 10⁹⁴(95-digit number)
21408331686927182803…89738360607629420799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.281 Γ— 10⁹⁴(95-digit number)
42816663373854365607…79476721215258841599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.563 Γ— 10⁹⁴(95-digit number)
85633326747708731215…58953442430517683199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.712 Γ— 10⁹⁡(96-digit number)
17126665349541746243…17906884861035366399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.425 Γ— 10⁹⁡(96-digit number)
34253330699083492486…35813769722070732799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.850 Γ— 10⁹⁡(96-digit number)
68506661398166984972…71627539444141465599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.370 Γ— 10⁹⁢(97-digit number)
13701332279633396994…43255078888282931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.740 Γ— 10⁹⁢(97-digit number)
27402664559266793989…86510157776565862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.480 Γ— 10⁹⁢(97-digit number)
54805329118533587978…73020315553131724799
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:57,757,780 XPMΒ·at block #6,814,213 Β· updates every 60s
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