Block #1,156,953

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/16/2015, 1:36:13 AM · Difficulty 10.9448 · 5,650,980 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9ffc215670ba14a422c475b3fecff846c6409a0c57fdfcf75cb82bb4d6371397

Height

#1,156,953

Difficulty

10.944812

Transactions

2

Size

427 B

Version

2

Bits

0af1df2e

Nonce

1,873,167,065

Timestamp

7/16/2015, 1:36:13 AM

Confirmations

5,650,980

Merkle Root

854cfb7b42fd782a014ae4ea345e8bb22b520e5bef1dc4bb711301132873994f
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.

2.546 × 10⁹⁴(95-digit number)
25468599184752706223…26830503023435939839
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
2.546 × 10⁹⁴(95-digit number)
25468599184752706223…26830503023435939839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.093 × 10⁹⁴(95-digit number)
50937198369505412446…53661006046871879679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.018 × 10⁹⁵(96-digit number)
10187439673901082489…07322012093743759359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.037 × 10⁹⁵(96-digit number)
20374879347802164978…14644024187487518719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.074 × 10⁹⁵(96-digit number)
40749758695604329957…29288048374975037439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.149 × 10⁹⁵(96-digit number)
81499517391208659914…58576096749950074879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.629 × 10⁹⁶(97-digit number)
16299903478241731982…17152193499900149759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.259 × 10⁹⁶(97-digit number)
32599806956483463965…34304386999800299519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.519 × 10⁹⁶(97-digit number)
65199613912966927931…68608773999600599039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.303 × 10⁹⁷(98-digit number)
13039922782593385586…37217547999201198079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.607 × 10⁹⁷(98-digit number)
26079845565186771172…74435095998402396159
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:57,707,502 XPM·at block #6,807,932 · updates every 60s
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