Block #1,382,672

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 12/24/2015, 8:26:15 AM · Difficulty 10.8086 · 5,434,644 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
57bb46016444341eb43b9f37c3a2cf02f651780c93f0c580d532c7ab82cb86f3

Height

#1,382,672

Difficulty

10.808624

Transactions

2

Size

1.28 KB

Version

2

Bits

0acf0200

Nonce

1,219,842,085

Timestamp

12/24/2015, 8:26:15 AM

Confirmations

5,434,644

Merkle Root

6e68f700b77eab1cb888d3be93d3c53a334b69a2c335c606ef4f8eba65232431
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.

1.020 × 10⁹⁵(96-digit number)
10209018611656339611…06510491175928445439
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
1.020 × 10⁹⁵(96-digit number)
10209018611656339611…06510491175928445439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.041 × 10⁹⁵(96-digit number)
20418037223312679222…13020982351856890879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.083 × 10⁹⁵(96-digit number)
40836074446625358445…26041964703713781759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.167 × 10⁹⁵(96-digit number)
81672148893250716891…52083929407427563519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.633 × 10⁹⁶(97-digit number)
16334429778650143378…04167858814855127039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.266 × 10⁹⁶(97-digit number)
32668859557300286756…08335717629710254079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.533 × 10⁹⁶(97-digit number)
65337719114600573513…16671435259420508159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.306 × 10⁹⁷(98-digit number)
13067543822920114702…33342870518841016319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.613 × 10⁹⁷(98-digit number)
26135087645840229405…66685741037682032639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.227 × 10⁹⁷(98-digit number)
52270175291680458810…33371482075364065279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.045 × 10⁹⁸(99-digit number)
10454035058336091762…66742964150728130559
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,782,573 XPM·at block #6,817,315 · updates every 60s
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