Block #1,245,411

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/20/2015, 10:11:15 PM · Difficulty 10.7457 · 5,560,595 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d5aae1f722f2827b9e4e09c5f4e4475b1a60e5447e58538315e50ba2f6e88781

Height

#1,245,411

Difficulty

10.745707

Transactions

4

Size

1.00 KB

Version

2

Bits

0abee6af

Nonce

301,047,352

Timestamp

9/20/2015, 10:11:15 PM

Confirmations

5,560,595

Merkle Root

dd9ac6e48f49c3647755863b0d4c0ce60f7a989259be0fd2278e710f581be05b
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.

2.641 × 10⁹³(94-digit number)
26415672559995242901…73578417466898798651
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
2.641 × 10⁹³(94-digit number)
26415672559995242901…73578417466898798651
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.283 × 10⁹³(94-digit number)
52831345119990485802…47156834933797597301
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.056 × 10⁹⁴(95-digit number)
10566269023998097160…94313669867595194601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.113 × 10⁹⁴(95-digit number)
21132538047996194320…88627339735190389201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.226 × 10⁹⁴(95-digit number)
42265076095992388641…77254679470380778401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.453 × 10⁹⁴(95-digit number)
84530152191984777283…54509358940761556801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.690 × 10⁹⁵(96-digit number)
16906030438396955456…09018717881523113601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.381 × 10⁹⁵(96-digit number)
33812060876793910913…18037435763046227201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.762 × 10⁹⁵(96-digit number)
67624121753587821826…36074871526092454401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.352 × 10⁹⁶(97-digit number)
13524824350717564365…72149743052184908801
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:57,692,126 XPM·at block #6,806,005 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.