Block #979,903

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/18/2015, 12:50:42 PM · Difficulty 10.8473 · 5,832,240 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a647eca08d92c921a9498b25f4a77df8d8ade7842f7040d3db3f5ea9ca0c9c4c

Height

#979,903

Difficulty

10.847265

Transactions

2

Size

869 B

Version

2

Bits

0ad8e662

Nonce

391,321,945

Timestamp

3/18/2015, 12:50:42 PM

Confirmations

5,832,240

Merkle Root

385a3ff65eded06e90b707b611f4f1a7bc44905fca3d38bd1bda44d1a1929de1
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.

2.157 × 10⁹⁴(95-digit number)
21576037093596802479…77121980667956940281
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
2.157 × 10⁹⁴(95-digit number)
21576037093596802479…77121980667956940281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.315 × 10⁹⁴(95-digit number)
43152074187193604959…54243961335913880561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.630 × 10⁹⁴(95-digit number)
86304148374387209918…08487922671827761121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.726 × 10⁹⁵(96-digit number)
17260829674877441983…16975845343655522241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.452 × 10⁹⁵(96-digit number)
34521659349754883967…33951690687311044481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.904 × 10⁹⁵(96-digit number)
69043318699509767934…67903381374622088961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.380 × 10⁹⁶(97-digit number)
13808663739901953586…35806762749244177921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.761 × 10⁹⁶(97-digit number)
27617327479803907173…71613525498488355841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.523 × 10⁹⁶(97-digit number)
55234654959607814347…43227050996976711681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.104 × 10⁹⁷(98-digit number)
11046930991921562869…86454101993953423361
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:57,741,159 XPM·at block #6,812,142 · updates every 60s
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