Block #760,327

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/10/2014, 11:29:55 AM · Difficulty 10.9717 · 6,066,246 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ca58594f464e6ddebaac5d6e256f23fff62ab0298ed6fadc5e8835d97e4b7299

Height

#760,327

Difficulty

10.971732

Transactions

3

Size

952 B

Version

2

Bits

0af8c366

Nonce

32,004,247

Timestamp

10/10/2014, 11:29:55 AM

Confirmations

6,066,246

Merkle Root

9f35f425be7ed7dd0b471376b1c4460866b90aade982d6caf6792a009d0adc95
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.

2.569 × 10⁹⁴(95-digit number)
25699422240078491500…03473167583066175881
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
2.569 × 10⁹⁴(95-digit number)
25699422240078491500…03473167583066175881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.139 × 10⁹⁴(95-digit number)
51398844480156983001…06946335166132351761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.027 × 10⁹⁵(96-digit number)
10279768896031396600…13892670332264703521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.055 × 10⁹⁵(96-digit number)
20559537792062793200…27785340664529407041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.111 × 10⁹⁵(96-digit number)
41119075584125586401…55570681329058814081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.223 × 10⁹⁵(96-digit number)
82238151168251172802…11141362658117628161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.644 × 10⁹⁶(97-digit number)
16447630233650234560…22282725316235256321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.289 × 10⁹⁶(97-digit number)
32895260467300469120…44565450632470512641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.579 × 10⁹⁶(97-digit number)
65790520934600938241…89130901264941025281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.315 × 10⁹⁷(98-digit number)
13158104186920187648…78261802529882050561
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:57,856,733 XPM·at block #6,826,572 · updates every 60s
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