Block #484,447

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 1:35:03 PM · Difficulty 10.5870 · 6,320,729 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4621d03ae8a49157a8e20b67aef1862c79e421a561ac7c8793b94c7caf4a536a

Height

#484,447

Difficulty

10.586990

Transactions

1

Size

765 B

Version

2

Bits

0a9644fd

Nonce

233,078

Timestamp

4/10/2014, 1:35:03 PM

Confirmations

6,320,729

Merkle Root

71d992f581a3a6f11a05b05ffd2e405e43bbd3e5f28d0022fe1fca5e6d95cd04
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.

8.247 × 10⁹⁴(95-digit number)
82478809774730158945…27261258286245729441
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
8.247 × 10⁹⁴(95-digit number)
82478809774730158945…27261258286245729441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.649 × 10⁹⁵(96-digit number)
16495761954946031789…54522516572491458881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.299 × 10⁹⁵(96-digit number)
32991523909892063578…09045033144982917761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.598 × 10⁹⁵(96-digit number)
65983047819784127156…18090066289965835521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.319 × 10⁹⁶(97-digit number)
13196609563956825431…36180132579931671041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.639 × 10⁹⁶(97-digit number)
26393219127913650862…72360265159863342081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.278 × 10⁹⁶(97-digit number)
52786438255827301725…44720530319726684161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.055 × 10⁹⁷(98-digit number)
10557287651165460345…89441060639453368321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.111 × 10⁹⁷(98-digit number)
21114575302330920690…78882121278906736641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.222 × 10⁹⁷(98-digit number)
42229150604661841380…57764242557813473281
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:57,685,476 XPM·at block #6,805,175 · updates every 60s
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