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Block #46,098

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2013, 5:12:01 AM Β· Difficulty 8.7811 Β· 6,770,675 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e8803559bf8c8ee7d81b0ae83722834f17ca68c0e7ac5a90f2e969bcaf2b6bdb
View on Chainz β†—

Height

#46,098

Difficulty

8.781113

Transactions

1

Size

201 B

Version

2

Bits

08c7f6fe

Nonce

36

Timestamp

7/15/2013, 5:12:01 AM

Confirmations

6,770,675

Mined by

⛏️ P2SHAJaStT14jmbiCKcmcHh8VAuZAUxoModEjU

Merkle Root

175d78bf7abf36f5dca31b56361e4e6f590c31424e664f966893fdf57b9b1582
Transactions (1)
Coinbase175d78bf7abf36…93fdf57b9b1582
1 in β†’ 1 out12.9500 XPM110 B
AJaStT14…xoModEjU
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.

4.004 Γ— 10⁹⁢(97-digit number)
40048041805866524088…74649993414051030459
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
4.004 Γ— 10⁹⁢(97-digit number)
40048041805866524088…74649993414051030459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.009 Γ— 10⁹⁢(97-digit number)
80096083611733048177…49299986828102060919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.601 Γ— 10⁹⁷(98-digit number)
16019216722346609635…98599973656204121839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.203 Γ— 10⁹⁷(98-digit number)
32038433444693219271…97199947312408243679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.407 Γ— 10⁹⁷(98-digit number)
64076866889386438542…94399894624816487359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.281 Γ— 10⁹⁸(99-digit number)
12815373377877287708…88799789249632974719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.563 Γ— 10⁹⁸(99-digit number)
25630746755754575416…77599578499265949439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.126 Γ— 10⁹⁸(99-digit number)
51261493511509150833…55199156998531898879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,778,218 XPMΒ·at block #6,816,772 Β· updates every 60s
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