Block #1,176,174

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/29/2015, 9:13:54 PM · Difficulty 10.9375 · 5,664,091 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c6432281a6685504f7ec93cf4d07c95c8ffb9098f9cfafac59820ed9afee49ee

Height

#1,176,174

Difficulty

10.937483

Transactions

6

Size

21.09 KB

Version

2

Bits

0aeffedf

Nonce

887,797,944

Timestamp

7/29/2015, 9:13:54 PM

Confirmations

5,664,091

Merkle Root

27210fff146c162100f82a9cdb75e267a555ceff2ce55b574b12848c27d33913
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.

6.110 × 10⁹⁵(96-digit number)
61109809532016427209…46919647213734023679
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
6.110 × 10⁹⁵(96-digit number)
61109809532016427209…46919647213734023679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.222 × 10⁹⁶(97-digit number)
12221961906403285441…93839294427468047359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.444 × 10⁹⁶(97-digit number)
24443923812806570883…87678588854936094719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.888 × 10⁹⁶(97-digit number)
48887847625613141767…75357177709872189439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.777 × 10⁹⁶(97-digit number)
97775695251226283535…50714355419744378879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.955 × 10⁹⁷(98-digit number)
19555139050245256707…01428710839488757759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.911 × 10⁹⁷(98-digit number)
39110278100490513414…02857421678977515519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.822 × 10⁹⁷(98-digit number)
78220556200981026828…05714843357955031039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.564 × 10⁹⁸(99-digit number)
15644111240196205365…11429686715910062079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.128 × 10⁹⁸(99-digit number)
31288222480392410731…22859373431820124159
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:57,966,434 XPM·at block #6,840,264 · updates every 60s
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