Block #1,240,752

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/17/2015, 1:03:51 PM · Difficulty 10.7558 · 5,570,221 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b87a004fb31f2a633eccc6a8e2c38b759d38ba627d1477fafc49b285235631fd

Height

#1,240,752

Difficulty

10.755821

Transactions

2

Size

425 B

Version

2

Bits

0ac17d80

Nonce

477,030,544

Timestamp

9/17/2015, 1:03:51 PM

Confirmations

5,570,221

Merkle Root

550a1dac7afa6e5a87d4f50776a8ab85d4c965e294325205cfe46675dad4595b
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.

1.440 × 10⁹⁴(95-digit number)
14400791047294842123…96834366494612685649
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
1.440 × 10⁹⁴(95-digit number)
14400791047294842123…96834366494612685649
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.880 × 10⁹⁴(95-digit number)
28801582094589684247…93668732989225371299
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.760 × 10⁹⁴(95-digit number)
57603164189179368495…87337465978450742599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.152 × 10⁹⁵(96-digit number)
11520632837835873699…74674931956901485199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.304 × 10⁹⁵(96-digit number)
23041265675671747398…49349863913802970399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.608 × 10⁹⁵(96-digit number)
46082531351343494796…98699727827605940799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.216 × 10⁹⁵(96-digit number)
92165062702686989592…97399455655211881599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.843 × 10⁹⁶(97-digit number)
18433012540537397918…94798911310423763199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.686 × 10⁹⁶(97-digit number)
36866025081074795837…89597822620847526399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.373 × 10⁹⁶(97-digit number)
73732050162149591674…79195645241695052799
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,731,886 XPM·at block #6,810,972 · updates every 60s
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