Block #479,655

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/7/2014, 7:45:20 PM · Difficulty 10.5099 · 6,327,413 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a002c113d16fcc358601377cc4eb5ba2d720f3f129b142d1bb55a99ca42d82b

Height

#479,655

Difficulty

10.509889

Transactions

1

Size

969 B

Version

2

Bits

0a828819

Nonce

11,562

Timestamp

4/7/2014, 7:45:20 PM

Confirmations

6,327,413

Merkle Root

b13ff47d2af6efa49c054cc2bf2f25eb5a7243626cb25f2d2bf7c05f0b52f956
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.

3.998 × 10⁹⁴(95-digit number)
39987810817813767669…05786342547251488641
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
3.998 × 10⁹⁴(95-digit number)
39987810817813767669…05786342547251488641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.997 × 10⁹⁴(95-digit number)
79975621635627535339…11572685094502977281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.599 × 10⁹⁵(96-digit number)
15995124327125507067…23145370189005954561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.199 × 10⁹⁵(96-digit number)
31990248654251014135…46290740378011909121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.398 × 10⁹⁵(96-digit number)
63980497308502028271…92581480756023818241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.279 × 10⁹⁶(97-digit number)
12796099461700405654…85162961512047636481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.559 × 10⁹⁶(97-digit number)
25592198923400811308…70325923024095272961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.118 × 10⁹⁶(97-digit number)
51184397846801622617…40651846048190545921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.023 × 10⁹⁷(98-digit number)
10236879569360324523…81303692096381091841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.047 × 10⁹⁷(98-digit number)
20473759138720649046…62607384192762183681
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:57,700,638 XPM·at block #6,807,067 · updates every 60s
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