Block #2,468,370

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/11/2018, 6:30:28 PM · Difficulty 10.9602 · 4,372,416 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
29710c0d812610e19d692a45b485e0ba15a0e415865e9220ab4cea9565cedbeb

Height

#2,468,370

Difficulty

10.960201

Transactions

2

Size

573 B

Version

2

Bits

0af5cfc2

Nonce

1,600,813,096

Timestamp

1/11/2018, 6:30:28 PM

Confirmations

4,372,416

Merkle Root

d4631f674cc1ca71d593ac70e6d99fb5eb7f1ce1d39e670152b5b35fc847883f
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.444 × 10⁹³(94-digit number)
24446057625537191922…61049156406813491199
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
2.444 × 10⁹³(94-digit number)
24446057625537191922…61049156406813491199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.889 × 10⁹³(94-digit number)
48892115251074383845…22098312813626982399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.778 × 10⁹³(94-digit number)
97784230502148767691…44196625627253964799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.955 × 10⁹⁴(95-digit number)
19556846100429753538…88393251254507929599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.911 × 10⁹⁴(95-digit number)
39113692200859507076…76786502509015859199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.822 × 10⁹⁴(95-digit number)
78227384401719014153…53573005018031718399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.564 × 10⁹⁵(96-digit number)
15645476880343802830…07146010036063436799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.129 × 10⁹⁵(96-digit number)
31290953760687605661…14292020072126873599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.258 × 10⁹⁵(96-digit number)
62581907521375211322…28584040144253747199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.251 × 10⁹⁶(97-digit number)
12516381504275042264…57168080288507494399
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,970,634 XPM·at block #6,840,785 · updates every 60s
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