Block #1,079,667

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/28/2015, 9:05:58 AM · Difficulty 10.7648 · 5,736,369 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0c4ebb35e6a9792553a0f7bad7a3b2772850832274b47788ec31f1a3d37eb6c6

Height

#1,079,667

Difficulty

10.764752

Transactions

2

Size

982 B

Version

2

Bits

0ac3c6d1

Nonce

1,112,894,431

Timestamp

5/28/2015, 9:05:58 AM

Confirmations

5,736,369

Merkle Root

573a4fdd0f77a1575f1c8414788adfa772e60f79e448121ca9e5a5cffdadf661
Transactions (2)
1 in → 1 out8.6300 XPM109 B
5 in → 1 out50.5980 XPM782 B
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.

1.021 × 10⁹⁶(97-digit number)
10214263220759867686…25424865708978279679
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
1.021 × 10⁹⁶(97-digit number)
10214263220759867686…25424865708978279679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.042 × 10⁹⁶(97-digit number)
20428526441519735372…50849731417956559359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.085 × 10⁹⁶(97-digit number)
40857052883039470745…01699462835913118719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.171 × 10⁹⁶(97-digit number)
81714105766078941491…03398925671826237439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.634 × 10⁹⁷(98-digit number)
16342821153215788298…06797851343652474879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.268 × 10⁹⁷(98-digit number)
32685642306431576596…13595702687304949759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.537 × 10⁹⁷(98-digit number)
65371284612863153193…27191405374609899519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.307 × 10⁹⁸(99-digit number)
13074256922572630638…54382810749219799039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.614 × 10⁹⁸(99-digit number)
26148513845145261277…08765621498439598079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.229 × 10⁹⁸(99-digit number)
52297027690290522554…17531242996879196159
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:57,772,402 XPM·at block #6,816,035 · updates every 60s
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