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Block #1,106,094

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/15/2015, 7:19:28 AM Β· Difficulty 10.7925 Β· 5,710,967 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0b82c84e6f394556c641f15c9d1e8abb5210ce885e25d3dbd4669cfb69acefe
View on Chainz β†—

Height

#1,106,094

Difficulty

10.792453

Transactions

2

Size

1.14 KB

Version

2

Bits

0acade3a

Nonce

318,605,485

Timestamp

6/15/2015, 7:19:28 AM

Confirmations

5,710,967

Mined by

⛏️ P2SHAcnBR4kUk6DHrnVAYFYdu7FN7Cz5drRXW6

Merkle Root

eae351c7b1204f935a53b1f1189da4771b7f46a69eb894d7070385694a4b5956
Transactions (2)
Coinbase5bde9d510fa74e…acad29a9dd01c1
1 in β†’ 1 out8.5800 XPM109 B
AcnBR4kU…z5drRXW6
bf2009231a5f0c…050ad5cff4730d
6 in β†’ 2 out6.8635 XPM968 B
Ae1BWyc3…FkXBXmm9AbecWDS9…1vtToSML
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.

1.381 Γ— 10⁹⁴(95-digit number)
13819737554113868087…45864822663868036379
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
1.381 Γ— 10⁹⁴(95-digit number)
13819737554113868087…45864822663868036379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.763 Γ— 10⁹⁴(95-digit number)
27639475108227736174…91729645327736072759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.527 Γ— 10⁹⁴(95-digit number)
55278950216455472348…83459290655472145519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.105 Γ— 10⁹⁡(96-digit number)
11055790043291094469…66918581310944291039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.211 Γ— 10⁹⁡(96-digit number)
22111580086582188939…33837162621888582079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.422 Γ— 10⁹⁡(96-digit number)
44223160173164377878…67674325243777164159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.844 Γ— 10⁹⁡(96-digit number)
88446320346328755757…35348650487554328319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.768 Γ— 10⁹⁢(97-digit number)
17689264069265751151…70697300975108656639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.537 Γ— 10⁹⁢(97-digit number)
35378528138531502303…41394601950217313279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.075 Γ— 10⁹⁢(97-digit number)
70757056277063004606…82789203900434626559
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:57,780,522 XPMΒ·at block #6,817,060 Β· updates every 60s
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