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Block #153,489

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 12:55:23 AM Β· Difficulty 9.8635 Β· 6,641,473 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
47d778b3e84c06bdfe61a9531c5bec45ad07ac38080f305a6290409dfacff0d4
View on Chainz β†—

Height

#153,489

Difficulty

9.863539

Transactions

2

Size

2.13 KB

Version

2

Bits

09dd10e1

Nonce

13,668

Timestamp

9/7/2013, 12:55:23 AM

Confirmations

6,641,473

Mined by

⛏️ P2SHAPte4D8c34JEczTgfzTznuC4bXWwSGVhpv

Merkle Root

bac664c38191d2d004a68cb867f51d8d1d3dbd53bc1b4b7a9afd894db65607fe
Transactions (2)
Coinbase8d481b45ea9123…b33c1e865dec09
1 in β†’ 1 out10.2900 XPM109 B
APte4D8c…WwSGVhpv
0bb95100dd3e2b…ded52d048396b4
17 in β†’ 1 out175.0700 XPM1.94 KB
AJs27LEf…M76myr9t
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.

1.166 Γ— 10⁹⁡(96-digit number)
11662736802426407231…71215254107992459521
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
1.166 Γ— 10⁹⁡(96-digit number)
11662736802426407231…71215254107992459521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.332 Γ— 10⁹⁡(96-digit number)
23325473604852814462…42430508215984919041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.665 Γ— 10⁹⁡(96-digit number)
46650947209705628924…84861016431969838081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.330 Γ— 10⁹⁡(96-digit number)
93301894419411257849…69722032863939676161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.866 Γ— 10⁹⁢(97-digit number)
18660378883882251569…39444065727879352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.732 Γ— 10⁹⁢(97-digit number)
37320757767764503139…78888131455758704641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.464 Γ— 10⁹⁢(97-digit number)
74641515535529006279…57776262911517409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.492 Γ— 10⁹⁷(98-digit number)
14928303107105801255…15552525823034818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.985 Γ— 10⁹⁷(98-digit number)
29856606214211602511…31105051646069637121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.971 Γ— 10⁹⁷(98-digit number)
59713212428423205023…62210103292139274241
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:57,603,734 XPMΒ·at block #6,794,961 Β· updates every 60s
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