Block #1,494,605

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/13/2016, 3:36:29 AM · Difficulty 10.6603 · 5,322,710 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd66112fd145f8b39642defc28fc2c2c8af52b9c59c7d81b0a0dc30d09925791

Height

#1,494,605

Difficulty

10.660294

Transactions

3

Size

4.04 KB

Version

2

Bits

0aa90902

Nonce

1,220,322,793

Timestamp

3/13/2016, 3:36:29 AM

Confirmations

5,322,710

Merkle Root

34926d5b1ffbe9ca1a0308e56092d92d45df8c88bc6e08b150e1aafb41e4704c
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.

6.133 × 10⁹⁵(96-digit number)
61336799499337817001…12870995857163468799
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
6.133 × 10⁹⁵(96-digit number)
61336799499337817001…12870995857163468799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.226 × 10⁹⁶(97-digit number)
12267359899867563400…25741991714326937599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.453 × 10⁹⁶(97-digit number)
24534719799735126800…51483983428653875199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.906 × 10⁹⁶(97-digit number)
49069439599470253601…02967966857307750399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.813 × 10⁹⁶(97-digit number)
98138879198940507202…05935933714615500799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.962 × 10⁹⁷(98-digit number)
19627775839788101440…11871867429231001599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.925 × 10⁹⁷(98-digit number)
39255551679576202881…23743734858462003199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.851 × 10⁹⁷(98-digit number)
78511103359152405762…47487469716924006399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.570 × 10⁹⁸(99-digit number)
15702220671830481152…94974939433848012799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.140 × 10⁹⁸(99-digit number)
31404441343660962304…89949878867696025599
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:57,782,565 XPM·at block #6,817,314 · updates every 60s
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