Block #607,325

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/29/2014, 10:32:51 PM · Difficulty 10.9072 · 6,207,528 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
abfbce7a483edc3da88972e53c00a294609db7478e60839141f34506fad5b5cc

Height

#607,325

Difficulty

10.907210

Transactions

3

Size

661 B

Version

2

Bits

0ae83ee2

Nonce

235,846,156

Timestamp

6/29/2014, 10:32:51 PM

Confirmations

6,207,528

Merkle Root

95eb1bdde337e930240b4c94a5e96043247d779e678d31b00b70e9bfe4101c93
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.

1.153 × 10¹⁰⁰(101-digit number)
11539998625907472562…45721287395390832641
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
1.153 × 10¹⁰⁰(101-digit number)
11539998625907472562…45721287395390832641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.307 × 10¹⁰⁰(101-digit number)
23079997251814945124…91442574790781665281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.615 × 10¹⁰⁰(101-digit number)
46159994503629890249…82885149581563330561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.231 × 10¹⁰⁰(101-digit number)
92319989007259780498…65770299163126661121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.846 × 10¹⁰¹(102-digit number)
18463997801451956099…31540598326253322241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.692 × 10¹⁰¹(102-digit number)
36927995602903912199…63081196652506644481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.385 × 10¹⁰¹(102-digit number)
73855991205807824399…26162393305013288961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.477 × 10¹⁰²(103-digit number)
14771198241161564879…52324786610026577921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.954 × 10¹⁰²(103-digit number)
29542396482323129759…04649573220053155841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.908 × 10¹⁰²(103-digit number)
59084792964646259519…09299146440106311681
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:57,762,907 XPM·at block #6,814,852 · 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.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy