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Block #726,661

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2014, 1:57:09 AM Β· Difficulty 10.9610 Β· 6,068,706 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a45de9eb3247408aafc7e84b267af7ebfff95da2da1872814f202003219ee211
View on Chainz β†—

Height

#726,661

Difficulty

10.961049

Transactions

2

Size

728 B

Version

2

Bits

0af60749

Nonce

654,221,176

Timestamp

9/18/2014, 1:57:09 AM

Confirmations

6,068,706

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f24d1620a96ccb9670293c0e07e5745e4af49df85f8f59e13a3b9b6bd321711b
Transactions (2)
Coinbase1864feb9738bb5…95a0af4349338f
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
825538878f70eb…62ab171c1ac982
3 in β†’ 2 out4999.9100 XPM522 B
AUyKm3Hc…w3ZnmXzUAcB1Cdou…cFjow1c5
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.

1.333 Γ— 10⁹⁡(96-digit number)
13338396406923591044…87583444529525220991
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
1.333 Γ— 10⁹⁡(96-digit number)
13338396406923591044…87583444529525220991
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.667 Γ— 10⁹⁡(96-digit number)
26676792813847182088…75166889059050441981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.335 Γ— 10⁹⁡(96-digit number)
53353585627694364176…50333778118100883961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.067 Γ— 10⁹⁢(97-digit number)
10670717125538872835…00667556236201767921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.134 Γ— 10⁹⁢(97-digit number)
21341434251077745670…01335112472403535841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.268 Γ— 10⁹⁢(97-digit number)
42682868502155491341…02670224944807071681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.536 Γ— 10⁹⁢(97-digit number)
85365737004310982682…05340449889614143361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.707 Γ— 10⁹⁷(98-digit number)
17073147400862196536…10680899779228286721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.414 Γ— 10⁹⁷(98-digit number)
34146294801724393073…21361799558456573441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.829 Γ— 10⁹⁷(98-digit number)
68292589603448786146…42723599116913146881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.365 Γ— 10⁹⁸(99-digit number)
13658517920689757229…85447198233826293761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,606,992 XPMΒ·at block #6,795,366 Β· updates every 60s
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