Block #147,547

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/3/2013, 4:27:35 AM · Difficulty 9.8522 · 6,662,785 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8594d7dc5c4a4d13aa6e9f9116231e02b2790e5ee764ce8f3ab01a09636f0f7a

Height

#147,547

Difficulty

9.852150

Transactions

2

Size

574 B

Version

2

Bits

09da2688

Nonce

75,227

Timestamp

9/3/2013, 4:27:35 AM

Confirmations

6,662,785

Merkle Root

0b3d2ef945e84d2d10f0ec6b14cab3d464226b51a088962e6657eecf66bcfcfd
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.

8.538 × 10⁹⁵(96-digit number)
85380604106911087942…87227544536661648401
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
8.538 × 10⁹⁵(96-digit number)
85380604106911087942…87227544536661648401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.707 × 10⁹⁶(97-digit number)
17076120821382217588…74455089073323296801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.415 × 10⁹⁶(97-digit number)
34152241642764435176…48910178146646593601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.830 × 10⁹⁶(97-digit number)
68304483285528870353…97820356293293187201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.366 × 10⁹⁷(98-digit number)
13660896657105774070…95640712586586374401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.732 × 10⁹⁷(98-digit number)
27321793314211548141…91281425173172748801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.464 × 10⁹⁷(98-digit number)
54643586628423096283…82562850346345497601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.092 × 10⁹⁸(99-digit number)
10928717325684619256…65125700692690995201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.185 × 10⁹⁸(99-digit number)
21857434651369238513…30251401385381990401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.371 × 10⁹⁸(99-digit number)
43714869302738477026…60502802770763980801
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:57,726,736 XPM·at block #6,810,331 · updates every 60s
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