Block #1,224,639

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/6/2015, 1:57:28 PM · Difficulty 10.7390 · 5,583,978 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c3e032828a529d43e6bf38279a4755dda1c41ea9c61e17bac1f8ccd2c4fc5747

Height

#1,224,639

Difficulty

10.738954

Transactions

5

Size

1.09 KB

Version

2

Bits

0abd2c1d

Nonce

159,840,809

Timestamp

9/6/2015, 1:57:28 PM

Confirmations

5,583,978

Merkle Root

63928318084ce052bff47c5042d59ca6d030a9283b453b8afbb8a965731ba26d
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.

2.703 × 10⁹⁶(97-digit number)
27036657873168188343…65374642761622566399
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
2.703 × 10⁹⁶(97-digit number)
27036657873168188343…65374642761622566399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.407 × 10⁹⁶(97-digit number)
54073315746336376686…30749285523245132799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.081 × 10⁹⁷(98-digit number)
10814663149267275337…61498571046490265599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.162 × 10⁹⁷(98-digit number)
21629326298534550674…22997142092980531199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.325 × 10⁹⁷(98-digit number)
43258652597069101348…45994284185961062399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.651 × 10⁹⁷(98-digit number)
86517305194138202697…91988568371922124799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.730 × 10⁹⁸(99-digit number)
17303461038827640539…83977136743844249599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.460 × 10⁹⁸(99-digit number)
34606922077655281079…67954273487688499199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.921 × 10⁹⁸(99-digit number)
69213844155310562158…35908546975376998399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.384 × 10⁹⁹(100-digit number)
13842768831062112431…71817093950753996799
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:57,712,986 XPM·at block #6,808,616 · updates every 60s
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