Block #1,225,070

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/6/2015, 9:45:11 PM · Difficulty 10.7370 · 5,584,313 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
318755e1c1c94e68d5993fc8fb1e600a52145398e3d0b467b0cad9df741d5baa

Height

#1,225,070

Difficulty

10.737043

Transactions

2

Size

433 B

Version

2

Bits

0abcaed3

Nonce

330,842,801

Timestamp

9/6/2015, 9:45:11 PM

Confirmations

5,584,313

Merkle Root

bd13859df055be522ec5f2f35bf7542e3ad7213c06e747d1817fd25a22f6c72f
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.

2.451 × 10⁹⁷(98-digit number)
24519426688885577533…20131619648792606719
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
2.451 × 10⁹⁷(98-digit number)
24519426688885577533…20131619648792606719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.903 × 10⁹⁷(98-digit number)
49038853377771155066…40263239297585213439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.807 × 10⁹⁷(98-digit number)
98077706755542310133…80526478595170426879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.961 × 10⁹⁸(99-digit number)
19615541351108462026…61052957190340853759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.923 × 10⁹⁸(99-digit number)
39231082702216924053…22105914380681707519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.846 × 10⁹⁸(99-digit number)
78462165404433848106…44211828761363415039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.569 × 10⁹⁹(100-digit number)
15692433080886769621…88423657522726830079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.138 × 10⁹⁹(100-digit number)
31384866161773539242…76847315045453660159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.276 × 10⁹⁹(100-digit number)
62769732323547078485…53694630090907320319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.255 × 10¹⁰⁰(101-digit number)
12553946464709415697…07389260181814640639
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:57,719,135 XPM·at block #6,809,382 · updates every 60s
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