Block #1,555,408

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/24/2016, 7:45:09 AM · Difficulty 10.6679 · 5,248,905 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
61977ed6b074208c22e2623dea27950a89eab3d0ca0e9f92863be34ad0fcf8f6

Height

#1,555,408

Difficulty

10.667937

Transactions

2

Size

4.90 KB

Version

2

Bits

0aaafdf0

Nonce

441,722,109

Timestamp

4/24/2016, 7:45:09 AM

Confirmations

5,248,905

Merkle Root

656c3de85189a5398fc6ea6c64bc9f9ac343ff2821bd713f9225e5e91e0b4ec2
Transactions (2)
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.

6.635 × 10⁹³(94-digit number)
66351875378594410223…62121770242989306881
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
6.635 × 10⁹³(94-digit number)
66351875378594410223…62121770242989306881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.327 × 10⁹⁴(95-digit number)
13270375075718882044…24243540485978613761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.654 × 10⁹⁴(95-digit number)
26540750151437764089…48487080971957227521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.308 × 10⁹⁴(95-digit number)
53081500302875528178…96974161943914455041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.061 × 10⁹⁵(96-digit number)
10616300060575105635…93948323887828910081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.123 × 10⁹⁵(96-digit number)
21232600121150211271…87896647775657820161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.246 × 10⁹⁵(96-digit number)
42465200242300422542…75793295551315640321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.493 × 10⁹⁵(96-digit number)
84930400484600845085…51586591102631280641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.698 × 10⁹⁶(97-digit number)
16986080096920169017…03173182205262561281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.397 × 10⁹⁶(97-digit number)
33972160193840338034…06346364410525122561
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:57,678,557 XPM·at block #6,804,312 · updates every 60s
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