Block #496,246

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/17/2014, 12:07:07 AM · Difficulty 10.7515 · 6,314,034 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1974b177750638973423df70a0f3f96b7e7b4aeb708bb635cf0541593f1cab13

Height

#496,246

Difficulty

10.751461

Transactions

5

Size

1.23 KB

Version

2

Bits

0ac05fc1

Nonce

271,745,145

Timestamp

4/17/2014, 12:07:07 AM

Confirmations

6,314,034

Merkle Root

c605fd63d5ecc26acef3b04a1e074dbb0f1a737e85b47ac9ebb0388d18ab4e15
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.

2.731 × 10¹⁰⁰(101-digit number)
27312562991859622055…08005862904102010879
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
2.731 × 10¹⁰⁰(101-digit number)
27312562991859622055…08005862904102010879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.462 × 10¹⁰⁰(101-digit number)
54625125983719244111…16011725808204021759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.092 × 10¹⁰¹(102-digit number)
10925025196743848822…32023451616408043519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.185 × 10¹⁰¹(102-digit number)
21850050393487697644…64046903232816087039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.370 × 10¹⁰¹(102-digit number)
43700100786975395289…28093806465632174079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.740 × 10¹⁰¹(102-digit number)
87400201573950790578…56187612931264348159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.748 × 10¹⁰²(103-digit number)
17480040314790158115…12375225862528696319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.496 × 10¹⁰²(103-digit number)
34960080629580316231…24750451725057392639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.992 × 10¹⁰²(103-digit number)
69920161259160632462…49500903450114785279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.398 × 10¹⁰³(104-digit number)
13984032251832126492…99001806900229570559
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:57,726,314 XPM·at block #6,810,279 · updates every 60s
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