Block #480,975

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/8/2014, 2:55:03 PM · Difficulty 10.5261 · 6,343,504 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3d68ca54700ac448db98ac82acdc8202a78f165ea0f61f3107d9956480dec257

Height

#480,975

Difficulty

10.526078

Transactions

5

Size

2.93 KB

Version

2

Bits

0a86ad0d

Nonce

81,888

Timestamp

4/8/2014, 2:55:03 PM

Confirmations

6,343,504

Merkle Root

691491bdbec76aeed81f12fe7409836a440273f5856f733a1c1c2f56837d687a
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.

4.979 × 10⁹⁴(95-digit number)
49796478743541477490…32916298920190170239
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
4.979 × 10⁹⁴(95-digit number)
49796478743541477490…32916298920190170239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.959 × 10⁹⁴(95-digit number)
99592957487082954981…65832597840380340479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.991 × 10⁹⁵(96-digit number)
19918591497416590996…31665195680760680959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.983 × 10⁹⁵(96-digit number)
39837182994833181992…63330391361521361919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.967 × 10⁹⁵(96-digit number)
79674365989666363985…26660782723042723839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.593 × 10⁹⁶(97-digit number)
15934873197933272797…53321565446085447679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.186 × 10⁹⁶(97-digit number)
31869746395866545594…06643130892170895359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.373 × 10⁹⁶(97-digit number)
63739492791733091188…13286261784341790719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.274 × 10⁹⁷(98-digit number)
12747898558346618237…26572523568683581439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.549 × 10⁹⁷(98-digit number)
25495797116693236475…53145047137367162879
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:57,839,903 XPM·at block #6,824,478 · updates every 60s
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