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Block #1,085,598

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/1/2015, 2:59:49 PM Β· Difficulty 10.7562 Β· 5,713,436 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aac3d0d565f1a69a3d065a6f739648db832fd1879c21970f62ae178daa16b8d7
View on Chainz β†—

Height

#1,085,598

Difficulty

10.756235

Transactions

1

Size

200 B

Version

2

Bits

0ac198a5

Nonce

90,529,893

Timestamp

6/1/2015, 2:59:49 PM

Confirmations

5,713,436

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

14652ce2412ca50aea8b9a14f6b7ca17451736a920e871318da480629a6b31a9
Transactions (1)
Coinbase14652ce2412ca5…a480629a6b31a9
1 in β†’ 1 out8.6300 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

4.583 Γ— 10⁹⁢(97-digit number)
45838662545258011043…02522692403647553999
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
4.583 Γ— 10⁹⁢(97-digit number)
45838662545258011043…02522692403647553999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.167 Γ— 10⁹⁢(97-digit number)
91677325090516022086…05045384807295107999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.833 Γ— 10⁹⁷(98-digit number)
18335465018103204417…10090769614590215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.667 Γ— 10⁹⁷(98-digit number)
36670930036206408834…20181539229180431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.334 Γ— 10⁹⁷(98-digit number)
73341860072412817669…40363078458360863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.466 Γ— 10⁹⁸(99-digit number)
14668372014482563533…80726156916721727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.933 Γ— 10⁹⁸(99-digit number)
29336744028965127067…61452313833443455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.867 Γ— 10⁹⁸(99-digit number)
58673488057930254135…22904627666886911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.173 Γ— 10⁹⁹(100-digit number)
11734697611586050827…45809255333773823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.346 Γ— 10⁹⁹(100-digit number)
23469395223172101654…91618510667547647999
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:57,636,311 XPMΒ·at block #6,799,033 Β· updates every 60s
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