Block #1,553,455

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/23/2016, 2:29:47 AM · Difficulty 10.6547 · 5,272,132 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c5e47a883607bd451cb72bdcec2bdcb153ac45be2d8a834afa11e0e03c6d8ce2

Height

#1,553,455

Difficulty

10.654691

Transactions

2

Size

832 B

Version

2

Bits

0aa799d8

Nonce

142,536,557

Timestamp

4/23/2016, 2:29:47 AM

Confirmations

5,272,132

Merkle Root

cd52ad7913520508950b7b1b6a5ce61820256dc5cd67c9d901c86f95fa28adb9
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.

8.140 × 10⁹⁴(95-digit number)
81404067973472840462…87835477343666679681
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
8.140 × 10⁹⁴(95-digit number)
81404067973472840462…87835477343666679681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.628 × 10⁹⁵(96-digit number)
16280813594694568092…75670954687333359361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.256 × 10⁹⁵(96-digit number)
32561627189389136184…51341909374666718721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.512 × 10⁹⁵(96-digit number)
65123254378778272369…02683818749333437441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.302 × 10⁹⁶(97-digit number)
13024650875755654473…05367637498666874881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.604 × 10⁹⁶(97-digit number)
26049301751511308947…10735274997333749761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.209 × 10⁹⁶(97-digit number)
52098603503022617895…21470549994667499521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.041 × 10⁹⁷(98-digit number)
10419720700604523579…42941099989334999041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.083 × 10⁹⁷(98-digit number)
20839441401209047158…85882199978669998081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.167 × 10⁹⁷(98-digit number)
41678882802418094316…71764399957339996161
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:57,848,795 XPM·at block #6,825,586 · updates every 60s
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