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Block #858,144

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/18/2014, 9:20:57 AM Β· Difficulty 10.9670 Β· 5,985,479 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3d5ecce5ce47556ed5fcb9ebd3225e26d68bed1d5f1d1983766d8e82d087b69d
View on Chainz β†—

Height

#858,144

Difficulty

10.967046

Transactions

2

Size

433 B

Version

2

Bits

0af7905b

Nonce

2,646,317,516

Timestamp

12/18/2014, 9:20:57 AM

Confirmations

5,985,479

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fa9c7e77c9bcc854bad83a49a72c0229c085c1fb2d9a8d1692e5a5cdddb472d9
Transactions (2)
Coinbase6bdb77b595c952…b61353911af6cf
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
c85bfd2885de19…601ac8139c866c
1 in β†’ 2 out0.1039 XPM226 B
AJu5LYAf…h3WsurLpAN6B1mSb…mN5dtaoF
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.

5.834 Γ— 10⁹⁢(97-digit number)
58349746694687919193…32948816092831865201
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
5.834 Γ— 10⁹⁢(97-digit number)
58349746694687919193…32948816092831865201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.166 Γ— 10⁹⁷(98-digit number)
11669949338937583838…65897632185663730401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.333 Γ— 10⁹⁷(98-digit number)
23339898677875167677…31795264371327460801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.667 Γ— 10⁹⁷(98-digit number)
46679797355750335355…63590528742654921601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.335 Γ— 10⁹⁷(98-digit number)
93359594711500670710…27181057485309843201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.867 Γ— 10⁹⁸(99-digit number)
18671918942300134142…54362114970619686401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.734 Γ— 10⁹⁸(99-digit number)
37343837884600268284…08724229941239372801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.468 Γ— 10⁹⁸(99-digit number)
74687675769200536568…17448459882478745601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.493 Γ— 10⁹⁹(100-digit number)
14937535153840107313…34896919764957491201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.987 Γ— 10⁹⁹(100-digit number)
29875070307680214627…69793839529914982401
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:57,993,350 XPMΒ·at block #6,843,622 Β· updates every 60s
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