Block #959,951

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/3/2015, 2:25:10 PM · Difficulty 10.8873 · 5,836,692 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e498c35251173c1f0887adde089cbdbed9a3c330b8d463963ca4c7a60703e6c0

Height

#959,951

Difficulty

10.887265

Transactions

5

Size

1.08 KB

Version

2

Bits

0ae323d3

Nonce

142,910,204

Timestamp

3/3/2015, 2:25:10 PM

Confirmations

5,836,692

Merkle Root

0e2640dd2d6d3b117c499d6ef2c6bd30f453c7f70903fbb9aef24c15df66294a
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.

7.615 × 10⁹⁴(95-digit number)
76157210350708014682…27298920618406439359
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
7.615 × 10⁹⁴(95-digit number)
76157210350708014682…27298920618406439359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.523 × 10⁹⁵(96-digit number)
15231442070141602936…54597841236812878719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.046 × 10⁹⁵(96-digit number)
30462884140283205872…09195682473625757439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.092 × 10⁹⁵(96-digit number)
60925768280566411745…18391364947251514879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.218 × 10⁹⁶(97-digit number)
12185153656113282349…36782729894503029759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.437 × 10⁹⁶(97-digit number)
24370307312226564698…73565459789006059519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.874 × 10⁹⁶(97-digit number)
48740614624453129396…47130919578012119039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.748 × 10⁹⁶(97-digit number)
97481229248906258793…94261839156024238079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.949 × 10⁹⁷(98-digit number)
19496245849781251758…88523678312048476159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.899 × 10⁹⁷(98-digit number)
38992491699562503517…77047356624096952319
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:57,617,146 XPM·at block #6,796,642 · updates every 60s
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