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Block #2,163,523

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/16/2017, 7:23:22 PM Β· Difficulty 10.8999 Β· 4,670,218 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
616254109fba53a409791a983d7b5e81c916c70c3b2cab200cde5ef161f6ce99
View on Chainz β†—

Height

#2,163,523

Difficulty

10.899890

Transactions

2

Size

6.63 KB

Version

2

Bits

0ae65f2d

Nonce

1,713,651,496

Timestamp

6/16/2017, 7:23:22 PM

Confirmations

4,670,218

Mined by

⛏️ P2SHAX8J2yfu4eL39eyexfa5q5ZQ4eoX3pysfN

Merkle Root

b36c456b92c04cdc3f06e0db4c9221cc1ed7989211475e7d8ce6a9b52802401c
Transactions (2)
Coinbase30551c56936bcc…793e159aa99d05
1 in β†’ 1 out8.4700 XPM110 B
AX8J2yfu…oX3pysfN
49709e3a3cf2fa…1085d2e006311e
44 in β†’ 2 out313.6421 XPM6.43 KB
AYAuRWxY…Rg3t4M63Ac71WKy3…3yXXi4Hh
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.

6.071 Γ— 10⁹⁴(95-digit number)
60719722340333805371…57074844434936985599
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
6.071 Γ— 10⁹⁴(95-digit number)
60719722340333805371…57074844434936985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.214 Γ— 10⁹⁡(96-digit number)
12143944468066761074…14149688869873971199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.428 Γ— 10⁹⁡(96-digit number)
24287888936133522148…28299377739747942399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.857 Γ— 10⁹⁡(96-digit number)
48575777872267044296…56598755479495884799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.715 Γ— 10⁹⁡(96-digit number)
97151555744534088593…13197510958991769599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.943 Γ— 10⁹⁢(97-digit number)
19430311148906817718…26395021917983539199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.886 Γ— 10⁹⁢(97-digit number)
38860622297813635437…52790043835967078399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.772 Γ— 10⁹⁢(97-digit number)
77721244595627270874…05580087671934156799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.554 Γ— 10⁹⁷(98-digit number)
15544248919125454174…11160175343868313599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.108 Γ— 10⁹⁷(98-digit number)
31088497838250908349…22320350687736627199
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:57,914,146 XPMΒ·at block #6,833,740 Β· updates every 60s
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