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Block #155,181

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 4:01:33 AM Β· Difficulty 9.8654 Β· 6,639,397 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09e2bb2c4a85a2d7331fe575cd5b8eb8eabf1fff9428a1b79e212d81398cb8c0
View on Chainz β†—

Height

#155,181

Difficulty

9.865400

Transactions

1

Size

197 B

Version

2

Bits

09dd8adb

Nonce

69,716

Timestamp

9/8/2013, 4:01:33 AM

Confirmations

6,639,397

Mined by

⛏️ P2SHAXFLhZGavKSLQwQxeg82k8FL6u9Bk5q7UH

Merkle Root

637050a16830101171d58358e151791540f77d563da9b832c83a1530349bdfa1
Transactions (1)
Coinbase637050a1683010…3a1530349bdfa1
1 in β†’ 1 out10.2600 XPM109 B
AXFLhZGa…9Bk5q7UH
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.170 Γ— 10⁹⁰(91-digit number)
21704133238299970701…00808387760789249841
Discovered Prime Numbers
p_k = 2^k Γ— 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
2.170 Γ— 10⁹⁰(91-digit number)
21704133238299970701…00808387760789249841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.340 Γ— 10⁹⁰(91-digit number)
43408266476599941402…01616775521578499681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.681 Γ— 10⁹⁰(91-digit number)
86816532953199882805…03233551043156999361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.736 Γ— 10⁹¹(92-digit number)
17363306590639976561…06467102086313998721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.472 Γ— 10⁹¹(92-digit number)
34726613181279953122…12934204172627997441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.945 Γ— 10⁹¹(92-digit number)
69453226362559906244…25868408345255994881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.389 Γ— 10⁹²(93-digit number)
13890645272511981248…51736816690511989761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.778 Γ— 10⁹²(93-digit number)
27781290545023962497…03473633381023979521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.556 Γ— 10⁹²(93-digit number)
55562581090047924995…06947266762047959041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,600,670 XPMΒ·at block #6,794,577 Β· updates every 60s
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