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Block #2,051,652

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/3/2017, 2:16:19 PM Β· Difficulty 10.7209 Β· 4,788,824 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
18f4c67fa0d98bc4799afb0f39a8513e00511e2ffb5139fe91c1d4fb8f8b483b
View on Chainz β†—

Height

#2,051,652

Difficulty

10.720869

Transactions

2

Size

4.75 KB

Version

2

Bits

0ab88ae1

Nonce

698,515,130

Timestamp

4/3/2017, 2:16:19 PM

Confirmations

4,788,824

Mined by

⛏️ P2SHAaRVuow4KoeJJ9GTAh8rBwT3EbQfTqPZAV

Merkle Root

0407f0a6b25ee8167145e4064c9c38af8927262efa36bc42da818b8ccb1befbe
Transactions (2)
Coinbase33da2573b2a39f…b4a4184e8e01c0
1 in β†’ 1 out8.7400 XPM109 B
AaRVuow4…QfTqPZAV
64c1d5ae37c4dd…fb5e8fb69da481
31 in β†’ 2 out514.8445 XPM4.56 KB
ANAy3gh2…EU3JsegRAKGxoSP8…8oH3hVLd
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.

2.091 Γ— 10⁹⁡(96-digit number)
20919705678868259399…45736935980080725921
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
2.091 Γ— 10⁹⁡(96-digit number)
20919705678868259399…45736935980080725921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.183 Γ— 10⁹⁡(96-digit number)
41839411357736518799…91473871960161451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.367 Γ— 10⁹⁡(96-digit number)
83678822715473037599…82947743920322903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.673 Γ— 10⁹⁢(97-digit number)
16735764543094607519…65895487840645807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.347 Γ— 10⁹⁢(97-digit number)
33471529086189215039…31790975681291614721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.694 Γ— 10⁹⁢(97-digit number)
66943058172378430079…63581951362583229441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13388611634475686015…27163902725166458881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.677 Γ— 10⁹⁷(98-digit number)
26777223268951372031…54327805450332917761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.355 Γ— 10⁹⁷(98-digit number)
53554446537902744063…08655610900665835521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.071 Γ— 10⁹⁸(99-digit number)
10710889307580548812…17311221801331671041
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:57,968,139 XPMΒ·at block #6,840,475 Β· updates every 60s
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