1. #6,810,8811CC11 primes

    Cunningham 1st · ⛏️ coinsforall.io

Block #466,179

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/29/2014, 11:55:39 PM · Difficulty 10.4221 · 6,344,703 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
73a1a1f4b19aa12db962d2da45c2411d4df824271411f8ba071530ad8a7fc8c8

Height

#466,179

Difficulty

10.422127

Transactions

2

Size

427 B

Version

2

Bits

0a6c107d

Nonce

9,179,013

Timestamp

3/29/2014, 11:55:39 PM

Confirmations

6,344,703

Merkle Root

0297893e03cb466b85723ebcf8a16604a877f3833d7861690318e4723142ba4e
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.

1.405 × 10⁹⁶(97-digit number)
14052063102051950078…40817196815242826241
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
1.405 × 10⁹⁶(97-digit number)
14052063102051950078…40817196815242826241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.810 × 10⁹⁶(97-digit number)
28104126204103900156…81634393630485652481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.620 × 10⁹⁶(97-digit number)
56208252408207800312…63268787260971304961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.124 × 10⁹⁷(98-digit number)
11241650481641560062…26537574521942609921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.248 × 10⁹⁷(98-digit number)
22483300963283120124…53075149043885219841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.496 × 10⁹⁷(98-digit number)
44966601926566240249…06150298087770439681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.993 × 10⁹⁷(98-digit number)
89933203853132480499…12300596175540879361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.798 × 10⁹⁸(99-digit number)
17986640770626496099…24601192351081758721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.597 × 10⁹⁸(99-digit number)
35973281541252992199…49202384702163517441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.194 × 10⁹⁸(99-digit number)
71946563082505984399…98404769404327034881
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,731,156 XPM·at block #6,810,881 · updates every 60s
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