Block #1,215,155

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/31/2015, 1:28:47 AM · Difficulty 10.7336 · 5,599,807 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
24fce05ad34916d8a58bf27a0ddef619346722caa00bac45f1131ec67f808d22

Height

#1,215,155

Difficulty

10.733607

Transactions

2

Size

391 B

Version

2

Bits

0abbcdb2

Nonce

94,887,757

Timestamp

8/31/2015, 1:28:47 AM

Confirmations

5,599,807

Merkle Root

a388195903fab2052bbafb2a4a94761e9db3acdbb627355e17d760fe64e61ccd
Transactions (2)
1 in → 1 out8.6800 XPM109 B
1 in → 1 out19.9900 XPM191 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.

3.404 × 10⁹⁶(97-digit number)
34043186609993117340…61784255000074542081
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
3.404 × 10⁹⁶(97-digit number)
34043186609993117340…61784255000074542081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.808 × 10⁹⁶(97-digit number)
68086373219986234681…23568510000149084161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.361 × 10⁹⁷(98-digit number)
13617274643997246936…47137020000298168321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.723 × 10⁹⁷(98-digit number)
27234549287994493872…94274040000596336641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.446 × 10⁹⁷(98-digit number)
54469098575988987745…88548080001192673281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.089 × 10⁹⁸(99-digit number)
10893819715197797549…77096160002385346561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.178 × 10⁹⁸(99-digit number)
21787639430395595098…54192320004770693121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.357 × 10⁹⁸(99-digit number)
43575278860791190196…08384640009541386241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.715 × 10⁹⁸(99-digit number)
87150557721582380392…16769280019082772481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.743 × 10⁹⁹(100-digit number)
17430111544316476078…33538560038165544961
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:57,763,791 XPM·at block #6,814,961 · updates every 60s
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