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Block #936,093

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/14/2015, 12:49:23 PM Β· Difficulty 10.9011 Β· 5,890,985 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31f3c0e6928eff8cee54ede0b695d20a453ce5a45a75b3b76ae4adf629cab289
View on Chainz β†—

Height

#936,093

Difficulty

10.901147

Transactions

1

Size

242 B

Version

2

Bits

0ae6b193

Nonce

207,036,806

Timestamp

2/14/2015, 12:49:23 PM

Confirmations

5,890,985

Mined by

⛏️ P2SHAVVmtV463g7Sm3ix3x9bkKaNbkewzQQzv3

Merkle Root

5bc65a64530c9e76a69f6e5af2db430a78548f9039a6f4b4e28ed02cb604ffe2
Transactions (1)
Coinbase5bc65a64530c9e…8ed02cb604ffe2
1 in β†’ 2 out8.4000 XPM152 B
AVVmtV46…ewzQQzv3ALPu3s2c…EJXLjVFh
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.

3.253 Γ— 10⁹⁴(95-digit number)
32539101414456867858…77013153157936159699
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
3.253 Γ— 10⁹⁴(95-digit number)
32539101414456867858…77013153157936159699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.507 Γ— 10⁹⁴(95-digit number)
65078202828913735717…54026306315872319399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.301 Γ— 10⁹⁡(96-digit number)
13015640565782747143…08052612631744638799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.603 Γ— 10⁹⁡(96-digit number)
26031281131565494287…16105225263489277599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.206 Γ— 10⁹⁡(96-digit number)
52062562263130988574…32210450526978555199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁢(97-digit number)
10412512452626197714…64420901053957110399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.082 Γ— 10⁹⁢(97-digit number)
20825024905252395429…28841802107914220799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.165 Γ— 10⁹⁢(97-digit number)
41650049810504790859…57683604215828441599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.330 Γ— 10⁹⁢(97-digit number)
83300099621009581718…15367208431656883199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁷(98-digit number)
16660019924201916343…30734416863313766399
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:57,860,808 XPMΒ·at block #6,827,077 Β· updates every 60s
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