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Block #2,004,572

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/1/2017, 6:49:26 PM Β· Difficulty 10.7269 Β· 4,803,351 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
acfde644587dfe859defc4026d679b925d6e7b9fc0ee077ccd76b5bdd14e254f
View on Chainz β†—

Height

#2,004,572

Difficulty

10.726902

Transactions

2

Size

1014 B

Version

2

Bits

0aba1645

Nonce

555,814,771

Timestamp

3/1/2017, 6:49:26 PM

Confirmations

4,803,351

Mined by

⛏️ P2SHAKKJ4ejHu2DPyLRcTopwn2nz28b915MZhX

Merkle Root

035c50edde1f5b0c6ee5a5438d067f1e8869e436ddda9ce27644ba842bee0194
Transactions (2)
Coinbased81f34fb14c4a0…1fe3a6133384ec
1 in β†’ 1 out8.6900 XPM109 B
AKKJ4ejH…b915MZhX
761004530de5ee…87a8d93d4d33e1
5 in β†’ 2 out11.7631 XPM815 B
AX36QtzB…59EAbBsTAbfHPQRP…cc1QCTYa
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.

3.812 Γ— 10⁹⁡(96-digit number)
38122678506002777012…99199678852962995201
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
3.812 Γ— 10⁹⁡(96-digit number)
38122678506002777012…99199678852962995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.624 Γ— 10⁹⁡(96-digit number)
76245357012005554024…98399357705925990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.524 Γ— 10⁹⁢(97-digit number)
15249071402401110804…96798715411851980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.049 Γ— 10⁹⁢(97-digit number)
30498142804802221609…93597430823703961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.099 Γ— 10⁹⁢(97-digit number)
60996285609604443219…87194861647407923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.219 Γ— 10⁹⁷(98-digit number)
12199257121920888643…74389723294815846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.439 Γ— 10⁹⁷(98-digit number)
24398514243841777287…48779446589631692801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.879 Γ— 10⁹⁷(98-digit number)
48797028487683554575…97558893179263385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.759 Γ— 10⁹⁷(98-digit number)
97594056975367109151…95117786358526771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.951 Γ— 10⁹⁸(99-digit number)
19518811395073421830…90235572717053542401
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:57,707,420 XPMΒ·at block #6,807,922 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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