Block #913,238

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2015, 12:53:57 PM · Difficulty 10.9276 · 5,878,387 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4a7a7495a76ea7491b6c615921710c5aafb3c64f17fcb687e703c1e9b4dbe42f

Height

#913,238

Difficulty

10.927639

Transactions

4

Size

62.15 KB

Version

2

Bits

0aed79b9

Nonce

571,830,585

Timestamp

1/28/2015, 12:53:57 PM

Confirmations

5,878,387

Merkle Root

072d1353c5feeffe0cb7d66adbf8c37f013a012cc8b806860fba79c1df320bb1
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.

6.123 × 10⁹³(94-digit number)
61234636644808458542…12759736776200957339
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
6.123 × 10⁹³(94-digit number)
61234636644808458542…12759736776200957339
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.224 × 10⁹⁴(95-digit number)
12246927328961691708…25519473552401914679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.449 × 10⁹⁴(95-digit number)
24493854657923383417…51038947104803829359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.898 × 10⁹⁴(95-digit number)
48987709315846766834…02077894209607658719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.797 × 10⁹⁴(95-digit number)
97975418631693533668…04155788419215317439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.959 × 10⁹⁵(96-digit number)
19595083726338706733…08311576838430634879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.919 × 10⁹⁵(96-digit number)
39190167452677413467…16623153676861269759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.838 × 10⁹⁵(96-digit number)
78380334905354826934…33246307353722539519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.567 × 10⁹⁶(97-digit number)
15676066981070965386…66492614707445079039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.135 × 10⁹⁶(97-digit number)
31352133962141930773…32985229414890158079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
6.270 × 10⁹⁶(97-digit number)
62704267924283861547…65970458829780316159
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:57,576,948 XPM·at block #6,791,624 · updates every 60s
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