Block #1,279,980

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/13/2015, 9:35:40 AM · Difficulty 10.8368 · 5,513,064 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be12187c5c7c80f38a5c3ce81bb146bfc170db5275c3aac5c9c31821ac2fc8bd

Height

#1,279,980

Difficulty

10.836802

Transactions

3

Size

800 B

Version

2

Bits

0ad638a3

Nonce

49,620,248

Timestamp

10/13/2015, 9:35:40 AM

Confirmations

5,513,064

Merkle Root

a018fa49bd7ca50227ee0ab32b8e50d9af38572ccb8e59d936580c3748d128d9
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.

1.042 × 10⁹⁴(95-digit number)
10423939058049276852…51042264205358915039
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
1.042 × 10⁹⁴(95-digit number)
10423939058049276852…51042264205358915039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.084 × 10⁹⁴(95-digit number)
20847878116098553704…02084528410717830079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.169 × 10⁹⁴(95-digit number)
41695756232197107409…04169056821435660159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.339 × 10⁹⁴(95-digit number)
83391512464394214819…08338113642871320319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.667 × 10⁹⁵(96-digit number)
16678302492878842963…16676227285742640639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.335 × 10⁹⁵(96-digit number)
33356604985757685927…33352454571485281279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.671 × 10⁹⁵(96-digit number)
66713209971515371855…66704909142970562559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.334 × 10⁹⁶(97-digit number)
13342641994303074371…33409818285941125119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.668 × 10⁹⁶(97-digit number)
26685283988606148742…66819636571882250239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.337 × 10⁹⁶(97-digit number)
53370567977212297484…33639273143764500479
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:57,588,342 XPM·at block #6,793,043 · updates every 60s
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