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Block #220,417

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 12:20:17 AM Β· Difficulty 9.9364 Β· 6,616,152 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c9053024fe46b2671a8bac09df23a442af531e1cd93c1ab2d0196b84080d982
View on Chainz β†—

Height

#220,417

Difficulty

9.936361

Transactions

2

Size

869 B

Version

2

Bits

09efb555

Nonce

93,459

Timestamp

10/21/2013, 12:20:17 AM

Confirmations

6,616,152

Mined by

⛏️ P2SHAGY68Nst9DeRc3u994LmE7NPPb3YWGhegP

Merkle Root

854ec31fb21a20f80f3a64f06b5e640b6519eb1cce8544fc6b5c12e2bee2aa33
Transactions (2)
Coinbaseed099713361f85…6cad712c89bd7c
1 in β†’ 1 out10.1300 XPM109 B
AGY68Nst…3YWGhegP
fcdc6ec515e3b4…5ecad8bac1b445
4 in β†’ 2 out125.3048 XPM669 B
AT4H1KdJ…9TGBV6wdAbpi6uu7…9D95uFUc
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.

7.217 Γ— 10⁹⁷(98-digit number)
72173917774759258531…99003834165628396921
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
7.217 Γ— 10⁹⁷(98-digit number)
72173917774759258531…99003834165628396921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.443 Γ— 10⁹⁸(99-digit number)
14434783554951851706…98007668331256793841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.886 Γ— 10⁹⁸(99-digit number)
28869567109903703412…96015336662513587681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.773 Γ— 10⁹⁸(99-digit number)
57739134219807406825…92030673325027175361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.154 Γ— 10⁹⁹(100-digit number)
11547826843961481365…84061346650054350721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.309 Γ— 10⁹⁹(100-digit number)
23095653687922962730…68122693300108701441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.619 Γ— 10⁹⁹(100-digit number)
46191307375845925460…36245386600217402881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.238 Γ— 10⁹⁹(100-digit number)
92382614751691850920…72490773200434805761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.847 Γ— 10¹⁰⁰(101-digit number)
18476522950338370184…44981546400869611521
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:57,936,817 XPMΒ·at block #6,836,568 Β· updates every 60s
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