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Block #2,292,313

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2017, 4:50:04 PM Β· Difficulty 10.9550 Β· 4,544,583 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00d81935688f0100fc3a76d64d288cc34661b734d2c15b2847a0cf36646b877d
View on Chainz β†—

Height

#2,292,313

Difficulty

10.954997

Transactions

2

Size

869 B

Version

2

Bits

0af47aaa

Nonce

932,913,116

Timestamp

9/11/2017, 4:50:04 PM

Confirmations

4,544,583

Mined by

⛏️ P2SHAbQ8ue3BeYrbr17WAa9XVXzZkRXoTS9tNK

Merkle Root

c336635c2095ee88a7f9cf765e74fd7add28c274218ef6070ecb3bafad28412d
Transactions (2)
Coinbase20af9a8c3b310e…8c3c3e3fd08196
1 in β†’ 1 out8.3300 XPM110 B
AbQ8ue3B…XoTS9tNK
5645b221135c10…641719cbc5e374
4 in β†’ 2 out2000.7987 XPM669 B
AVarMMq5…BQv6UCibARaNCeSx…b8M3uhxY
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.

5.114 Γ— 10⁹⁴(95-digit number)
51142344219349108538…72182217998118476681
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
5.114 Γ— 10⁹⁴(95-digit number)
51142344219349108538…72182217998118476681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.022 Γ— 10⁹⁡(96-digit number)
10228468843869821707…44364435996236953361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.045 Γ— 10⁹⁡(96-digit number)
20456937687739643415…88728871992473906721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.091 Γ— 10⁹⁡(96-digit number)
40913875375479286831…77457743984947813441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.182 Γ— 10⁹⁡(96-digit number)
81827750750958573662…54915487969895626881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.636 Γ— 10⁹⁢(97-digit number)
16365550150191714732…09830975939791253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.273 Γ— 10⁹⁢(97-digit number)
32731100300383429464…19661951879582507521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.546 Γ— 10⁹⁢(97-digit number)
65462200600766858929…39323903759165015041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.309 Γ— 10⁹⁷(98-digit number)
13092440120153371785…78647807518330030081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.618 Γ— 10⁹⁷(98-digit number)
26184880240306743571…57295615036660060161
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:57,939,462 XPMΒ·at block #6,836,895 Β· updates every 60s
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