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Block #86,935

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2013, 12:19:19 PM Β· Difficulty 9.2841 Β· 6,717,133 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0a76ee21bdb898ffae33239207afc93ac6dd9605112ae6e9407c64b67ab2307
View on Chainz β†—

Height

#86,935

Difficulty

9.284084

Transactions

1

Size

201 B

Version

2

Bits

0948b9c0

Nonce

61,543

Timestamp

7/28/2013, 12:19:19 PM

Confirmations

6,717,133

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

f459d5d03483efa248c538d99a6d3e7057bf87080c664d5a7d2c6dab1e1f61ce
Transactions (1)
Coinbasef459d5d03483ef…2c6dab1e1f61ce
1 in β†’ 1 out11.5900 XPM109 B
ATe7tG7X…yczDSDEp
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.

3.904 Γ— 10⁹⁸(99-digit number)
39041367106507225251…93948274859267991829
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
3.904 Γ— 10⁹⁸(99-digit number)
39041367106507225251…93948274859267991829
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.808 Γ— 10⁹⁸(99-digit number)
78082734213014450503…87896549718535983659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.561 Γ— 10⁹⁹(100-digit number)
15616546842602890100…75793099437071967319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.123 Γ— 10⁹⁹(100-digit number)
31233093685205780201…51586198874143934639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.246 Γ— 10⁹⁹(100-digit number)
62466187370411560402…03172397748287869279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.249 Γ— 10¹⁰⁰(101-digit number)
12493237474082312080…06344795496575738559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.498 Γ— 10¹⁰⁰(101-digit number)
24986474948164624161…12689590993151477119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.997 Γ— 10¹⁰⁰(101-digit number)
49972949896329248322…25379181986302954239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.994 Γ— 10¹⁰⁰(101-digit number)
99945899792658496644…50758363972605908479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,676,599 XPMΒ·at block #6,804,067 Β· updates every 60s
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