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Block #2,233,817

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/2/2017, 2:16:53 PM Β· Difficulty 10.9459 Β· 4,571,346 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4c3f54df71d7ea26e5e91fbe76b49410d77557a7ed4f5a8a072a5bb319de23de
View on Chainz β†—

Height

#2,233,817

Difficulty

10.945895

Transactions

2

Size

392 B

Version

2

Bits

0af22627

Nonce

376,933,383

Timestamp

8/2/2017, 2:16:53 PM

Confirmations

4,571,346

Mined by

⛏️ P2SHAehk1ZFkrZY7N7xJMDDLUPshQhFHtC1zgM

Merkle Root

4cadd16e99858ff9d8058adf64683df553f651cee6223576061faf44ea2a6fbb
Transactions (2)
Coinbase4fc640ac9a07fb…2ff06430db6d59
1 in β†’ 1 out8.3400 XPM110 B
Aehk1ZFk…FHtC1zgM
a16f516d09072c…33d6893aee9d7e
1 in β†’ 1 out0.4543 XPM192 B
AWucUP8L…iHfAHKLR
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.

1.409 Γ— 10⁹⁴(95-digit number)
14098141825537126675…05684078206182240279
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.409 Γ— 10⁹⁴(95-digit number)
14098141825537126675…05684078206182240279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.819 Γ— 10⁹⁴(95-digit number)
28196283651074253351…11368156412364480559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.639 Γ— 10⁹⁴(95-digit number)
56392567302148506703…22736312824728961119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.127 Γ— 10⁹⁡(96-digit number)
11278513460429701340…45472625649457922239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.255 Γ— 10⁹⁡(96-digit number)
22557026920859402681…90945251298915844479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.511 Γ— 10⁹⁡(96-digit number)
45114053841718805362…81890502597831688959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.022 Γ— 10⁹⁡(96-digit number)
90228107683437610725…63781005195663377919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.804 Γ— 10⁹⁢(97-digit number)
18045621536687522145…27562010391326755839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.609 Γ— 10⁹⁢(97-digit number)
36091243073375044290…55124020782653511679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.218 Γ— 10⁹⁢(97-digit number)
72182486146750088580…10248041565307023359
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,685,371 XPMΒ·at block #6,805,162 Β· updates every 60s
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