Block #479,953

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/8/2014, 12:31:11 AM · Difficulty 10.5111 · 6,347,014 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2e4ca281c1e0b223b5c03421f836ea3ee7fb75e9c2fb9b4c97df8c540e501dae

Height

#479,953

Difficulty

10.511119

Transactions

1

Size

905 B

Version

2

Bits

0a82d8aa

Nonce

93,771

Timestamp

4/8/2014, 12:31:11 AM

Confirmations

6,347,014

Merkle Root

5a595753b5c23e1fbf1bc33dd5900e5fe397757fc5de12eb1a0d60cdbd4d1376
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.

1.272 × 10¹⁰⁵(106-digit number)
12723233478077645536…60089785177820450561
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
1.272 × 10¹⁰⁵(106-digit number)
12723233478077645536…60089785177820450561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.544 × 10¹⁰⁵(106-digit number)
25446466956155291073…20179570355640901121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.089 × 10¹⁰⁵(106-digit number)
50892933912310582147…40359140711281802241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.017 × 10¹⁰⁶(107-digit number)
10178586782462116429…80718281422563604481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.035 × 10¹⁰⁶(107-digit number)
20357173564924232858…61436562845127208961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.071 × 10¹⁰⁶(107-digit number)
40714347129848465717…22873125690254417921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.142 × 10¹⁰⁶(107-digit number)
81428694259696931435…45746251380508835841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.628 × 10¹⁰⁷(108-digit number)
16285738851939386287…91492502761017671681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.257 × 10¹⁰⁷(108-digit number)
32571477703878772574…82985005522035343361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.514 × 10¹⁰⁷(108-digit number)
65142955407757545148…65970011044070686721
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:57,859,913 XPM·at block #6,826,966 · updates every 60s
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