Block #1,207,001

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/24/2015, 5:55:45 PM · Difficulty 10.7786 · 5,598,862 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fb9f0137db1c4bd9ee76ddf3f6eafdb15c543ef9d549c7385457f222e561b3a

Height

#1,207,001

Difficulty

10.778614

Transactions

2

Size

952 B

Version

2

Bits

0ac7533a

Nonce

808,572,077

Timestamp

8/24/2015, 5:55:45 PM

Confirmations

5,598,862

Merkle Root

dc29c1167b12e9782f1b71f5c5fd7f565a5171f78cab11ffc9098227f8f34fab
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.

7.777 × 10⁹⁵(96-digit number)
77772242063232287231…88513796416429529601
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
7.777 × 10⁹⁵(96-digit number)
77772242063232287231…88513796416429529601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.555 × 10⁹⁶(97-digit number)
15554448412646457446…77027592832859059201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.110 × 10⁹⁶(97-digit number)
31108896825292914892…54055185665718118401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.221 × 10⁹⁶(97-digit number)
62217793650585829784…08110371331436236801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.244 × 10⁹⁷(98-digit number)
12443558730117165956…16220742662872473601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.488 × 10⁹⁷(98-digit number)
24887117460234331913…32441485325744947201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.977 × 10⁹⁷(98-digit number)
49774234920468663827…64882970651489894401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.954 × 10⁹⁷(98-digit number)
99548469840937327655…29765941302979788801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.990 × 10⁹⁸(99-digit number)
19909693968187465531…59531882605959577601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.981 × 10⁹⁸(99-digit number)
39819387936374931062…19063765211919155201
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,690,986 XPM·at block #6,805,862 · updates every 60s
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