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Block #545,980

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2014, 3:41:39 PM Β· Difficulty 10.9549 Β· 6,297,210 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d504a1d9da4120b78ebc350ed405b097565b119bd1a0367d0a410bb0a30c2a3
View on Chainz β†—

Height

#545,980

Difficulty

10.954864

Transactions

1

Size

243 B

Version

2

Bits

0af471fd

Nonce

3,389,043,918

Timestamp

5/15/2014, 3:41:39 PM

Confirmations

6,297,210

Mined by

⛏️ P2SHAZ1U8y3e2uRnnjvTyEBzVACUNiCyU6Gm24

Merkle Root

0f7d42841e3a3a21c346466d387f66b685fff8136c18d2872206904a93e182ba
Transactions (1)
Coinbase0f7d42841e3a3a…06904a93e182ba
1 in β†’ 2 out8.3200 XPM152 B
AZ1U8y3e…CyU6Gm24ALPu3s2c…EJXLjVFh
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.

1.129 Γ— 10⁹⁸(99-digit number)
11298983954890435290…74447289109578833391
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
1.129 Γ— 10⁹⁸(99-digit number)
11298983954890435290…74447289109578833391
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.259 Γ— 10⁹⁸(99-digit number)
22597967909780870580…48894578219157666781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.519 Γ— 10⁹⁸(99-digit number)
45195935819561741161…97789156438315333561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.039 Γ— 10⁹⁸(99-digit number)
90391871639123482322…95578312876630667121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.807 Γ— 10⁹⁹(100-digit number)
18078374327824696464…91156625753261334241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.615 Γ— 10⁹⁹(100-digit number)
36156748655649392928…82313251506522668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.231 Γ— 10⁹⁹(100-digit number)
72313497311298785857…64626503013045336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.446 Γ— 10¹⁰⁰(101-digit number)
14462699462259757171…29253006026090673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.892 Γ— 10¹⁰⁰(101-digit number)
28925398924519514343…58506012052181347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.785 Γ— 10¹⁰⁰(101-digit number)
57850797849039028686…17012024104362695681
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:57,989,889 XPMΒ·at block #6,843,189 Β· updates every 60s
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