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Block #118,949

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2013, 3:44:43 AM Β· Difficulty 9.7492 Β· 6,698,135 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c47556663ca3ca4c2b61a57b02ef65202f5c02cff59eff30ea53bed1ee958473
View on Chainz β†—

Height

#118,949

Difficulty

9.749186

Transactions

1

Size

201 B

Version

2

Bits

09bfcaaf

Nonce

103,329

Timestamp

8/16/2013, 3:44:43 AM

Confirmations

6,698,135

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

f19f51454ead78e45abf8562e6bf3135f886c03b72425560df889046dbddac58
Transactions (1)
Coinbasef19f51454ead78…889046dbddac58
1 in β†’ 1 out10.5100 XPM109 B
AeEXQxqG…J2q5dxWc
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.

3.454 Γ— 10⁹⁸(99-digit number)
34548491350679289456…86461924474724951059
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
3.454 Γ— 10⁹⁸(99-digit number)
34548491350679289456…86461924474724951059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.909 Γ— 10⁹⁸(99-digit number)
69096982701358578913…72923848949449902119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.381 Γ— 10⁹⁹(100-digit number)
13819396540271715782…45847697898899804239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.763 Γ— 10⁹⁹(100-digit number)
27638793080543431565…91695395797799608479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.527 Γ— 10⁹⁹(100-digit number)
55277586161086863131…83390791595599216959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.105 Γ— 10¹⁰⁰(101-digit number)
11055517232217372626…66781583191198433919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.211 Γ— 10¹⁰⁰(101-digit number)
22111034464434745252…33563166382396867839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.422 Γ— 10¹⁰⁰(101-digit number)
44222068928869490504…67126332764793735679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.844 Γ— 10¹⁰⁰(101-digit number)
88444137857738981009…34252665529587471359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.768 Γ— 10¹⁰¹(102-digit number)
17688827571547796201…68505331059174942719
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:57,780,710 XPMΒ·at block #6,817,083 Β· updates every 60s
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