Block #792,383

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/1/2014, 4:03:53 PM · Difficulty 10.9735 · 6,020,619 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fcb5dffda6d95d84c0932f2c16831d3f0727fc5a0ce43e38dec726ddcb12a021

Height

#792,383

Difficulty

10.973544

Transactions

3

Size

658 B

Version

2

Bits

0af93a2d

Nonce

382,191,973

Timestamp

11/1/2014, 4:03:53 PM

Confirmations

6,020,619

Merkle Root

81f2c8b815d7025c366ffb8fe96655b56955283825938acc538551a080fe9c0b
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.

5.390 × 10⁹⁵(96-digit number)
53903287359849149330…45412527720829121281
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
5.390 × 10⁹⁵(96-digit number)
53903287359849149330…45412527720829121281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.078 × 10⁹⁶(97-digit number)
10780657471969829866…90825055441658242561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.156 × 10⁹⁶(97-digit number)
21561314943939659732…81650110883316485121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.312 × 10⁹⁶(97-digit number)
43122629887879319464…63300221766632970241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.624 × 10⁹⁶(97-digit number)
86245259775758638929…26600443533265940481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.724 × 10⁹⁷(98-digit number)
17249051955151727785…53200887066531880961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.449 × 10⁹⁷(98-digit number)
34498103910303455571…06401774133063761921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.899 × 10⁹⁷(98-digit number)
68996207820606911143…12803548266127523841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.379 × 10⁹⁸(99-digit number)
13799241564121382228…25607096532255047681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.759 × 10⁹⁸(99-digit number)
27598483128242764457…51214193064510095361
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:57,748,056 XPM·at block #6,813,001 · updates every 60s
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