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Block #181,306

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2013, 11:48:53 AM Β· Difficulty 9.8597 Β· 6,614,501 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
84d6919a8a17478dca573c520b797c7b7fa738e5f3654053921ebbf805f4423f
View on Chainz β†—

Height

#181,306

Difficulty

9.859712

Transactions

2

Size

3.55 KB

Version

2

Bits

09dc161c

Nonce

29,178

Timestamp

9/26/2013, 11:48:53 AM

Confirmations

6,614,501

Mined by

⛏️ P2SHAQGR5mjpPL7Tku6ZpKsqq68CHtk2qiZtZC

Merkle Root

511dea3562caeefe2e9b95fb0e0fcf328127eb9c101abd856dbc6d5393d1ab2c
Transactions (2)
Coinbase5b9f685f055f2d…015f6fe4a76d61
1 in β†’ 1 out10.3100 XPM109 B
AQGR5mjp…k2qiZtZC
1788eb600fc39a…f3ef83f91a082a
23 in β†’ 1 out88.0388 XPM3.36 KB
Ac6AHy6P…obQfLyE8
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.

1.822 Γ— 10⁹³(94-digit number)
18226933962550680023…20572967077657152641
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
1.822 Γ— 10⁹³(94-digit number)
18226933962550680023…20572967077657152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.645 Γ— 10⁹³(94-digit number)
36453867925101360047…41145934155314305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.290 Γ— 10⁹³(94-digit number)
72907735850202720095…82291868310628610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.458 Γ— 10⁹⁴(95-digit number)
14581547170040544019…64583736621257221121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.916 Γ— 10⁹⁴(95-digit number)
29163094340081088038…29167473242514442241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.832 Γ— 10⁹⁴(95-digit number)
58326188680162176076…58334946485028884481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.166 Γ— 10⁹⁡(96-digit number)
11665237736032435215…16669892970057768961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.333 Γ— 10⁹⁡(96-digit number)
23330475472064870430…33339785940115537921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.666 Γ— 10⁹⁡(96-digit number)
46660950944129740861…66679571880231075841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.332 Γ— 10⁹⁡(96-digit number)
93321901888259481722…33359143760462151681
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,610,535 XPMΒ·at block #6,795,806 Β· updates every 60s
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