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Block #2,165,337

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/18/2017, 3:01:00 AM Β· Difficulty 10.8982 Β· 4,642,699 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b04f5ce34a764c6c5c35e0ffd60bbfea530f474605fdadf2d2d530f5d9edd603
View on Chainz β†—

Height

#2,165,337

Difficulty

10.898234

Transactions

2

Size

3.14 KB

Version

2

Bits

0ae5f2a9

Nonce

303,577,773

Timestamp

6/18/2017, 3:01:00 AM

Confirmations

4,642,699

Mined by

⛏️ P2SHAJgAmjdhHE61jhgem4zmViGKpMonFgUFe2

Merkle Root

fb45e960792a605848773e96ca893700b684c69f6496eb2c9fa660824573d90a
Transactions (2)
Coinbasec95c31b13d402c…80f1bbfabaab03
1 in β†’ 1 out8.4500 XPM110 B
AJgAmjdh…onFgUFe2
04a92462fa2df7…3f2fd8f4916d7d
20 in β†’ 1 out398.0200 XPM2.94 KB
AMtnaR5m…zWAw7GA1
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.

5.611 Γ— 10⁹²(93-digit number)
56110198505193999208…82527294316905574399
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
5.611 Γ— 10⁹²(93-digit number)
56110198505193999208…82527294316905574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.122 Γ— 10⁹³(94-digit number)
11222039701038799841…65054588633811148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.244 Γ— 10⁹³(94-digit number)
22444079402077599683…30109177267622297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.488 Γ— 10⁹³(94-digit number)
44888158804155199367…60218354535244595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.977 Γ— 10⁹³(94-digit number)
89776317608310398734…20436709070489190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.795 Γ— 10⁹⁴(95-digit number)
17955263521662079746…40873418140978380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.591 Γ— 10⁹⁴(95-digit number)
35910527043324159493…81746836281956761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.182 Γ— 10⁹⁴(95-digit number)
71821054086648318987…63493672563913523199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁡(96-digit number)
14364210817329663797…26987345127827046399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.872 Γ— 10⁹⁡(96-digit number)
28728421634659327594…53974690255654092799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.745 Γ— 10⁹⁡(96-digit number)
57456843269318655189…07949380511308185599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,708,333 XPMΒ·at block #6,808,035 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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