Block #1,418,551

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2016, 12:13:14 PM · Difficulty 10.7962 · 5,399,158 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fe7588b4a0b841df529e6ac16dbfbfc1abd4115a9f058164c531723bf9e36384

Height

#1,418,551

Difficulty

10.796152

Transactions

2

Size

903 B

Version

2

Bits

0acbd09c

Nonce

1,147,953,773

Timestamp

1/18/2016, 12:13:14 PM

Confirmations

5,399,158

Merkle Root

743bf8989a9f87e1ae34983968770da10f022619a7eff44f7b3dbfeca413098e
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.

1.583 × 10⁹⁶(97-digit number)
15834729131553921799…43770314461741178881
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
1.583 × 10⁹⁶(97-digit number)
15834729131553921799…43770314461741178881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.166 × 10⁹⁶(97-digit number)
31669458263107843598…87540628923482357761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.333 × 10⁹⁶(97-digit number)
63338916526215687196…75081257846964715521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.266 × 10⁹⁷(98-digit number)
12667783305243137439…50162515693929431041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.533 × 10⁹⁷(98-digit number)
25335566610486274878…00325031387858862081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.067 × 10⁹⁷(98-digit number)
50671133220972549757…00650062775717724161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.013 × 10⁹⁸(99-digit number)
10134226644194509951…01300125551435448321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.026 × 10⁹⁸(99-digit number)
20268453288389019902…02600251102870896641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.053 × 10⁹⁸(99-digit number)
40536906576778039805…05200502205741793281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.107 × 10⁹⁸(99-digit number)
81073813153556079611…10401004411483586561
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:57,785,731 XPM·at block #6,817,708 · updates every 60s
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