XPM Prime Explorer symbol
XPMPrime Explorer

Block #70,143

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 12:11:12 PM Β· Difficulty 8.9918 Β· 6,724,707 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5bb79f2d3ea294562441fd5a8fd5ab30c11811c28a26a05272e91efd215a77ab
View on Chainz β†—

Height

#70,143

Difficulty

8.991808

Transactions

1

Size

202 B

Version

2

Bits

08fde726

Nonce

879

Timestamp

7/20/2013, 12:11:12 PM

Confirmations

6,724,707

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

b587743a253b73d6d3e861eae6d46f03b6d79f1400f0d129930087141f7324b7
Transactions (1)
Coinbaseb587743a253b73…0087141f7324b7
1 in β†’ 1 out12.3500 XPM110 B
AXSFye4r…ADf1YWCU
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.

6.441 Γ— 10⁹⁹(100-digit number)
64410322225412780968…29526111657801472479
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
6.441 Γ— 10⁹⁹(100-digit number)
64410322225412780968…29526111657801472479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.288 Γ— 10¹⁰⁰(101-digit number)
12882064445082556193…59052223315602944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.576 Γ— 10¹⁰⁰(101-digit number)
25764128890165112387…18104446631205889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.152 Γ— 10¹⁰⁰(101-digit number)
51528257780330224775…36208893262411779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.030 Γ— 10¹⁰¹(102-digit number)
10305651556066044955…72417786524823559679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.061 Γ— 10¹⁰¹(102-digit number)
20611303112132089910…44835573049647119359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.122 Γ— 10¹⁰¹(102-digit number)
41222606224264179820…89671146099294238719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.244 Γ— 10¹⁰¹(102-digit number)
82445212448528359640…79342292198588477439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.648 Γ— 10¹⁰²(103-digit number)
16489042489705671928…58684584397176954879
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:57,602,829 XPMΒ·at block #6,794,849 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK