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Block #2,158,323

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2017, 12:10:56 AM Β· Difficulty 10.9050 Β· 4,684,700 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ebf3e6ada1b1f8c577f353686e634b0c35a22bfbd53d1d02a183b24da1d00bc
View on Chainz β†—

Height

#2,158,323

Difficulty

10.904959

Transactions

2

Size

1.43 KB

Version

2

Bits

0ae7ab6a

Nonce

256,991,969

Timestamp

6/13/2017, 12:10:56 AM

Confirmations

4,684,700

Mined by

⛏️ P2SHAGvRfDpzvRr6cc8ZheNfMwNq7k1i6rPddM

Merkle Root

8bcfff385b80e3a6911a58a0adf78f57d2d49c58e7e76d901164f49b0d36726f
Transactions (2)
Coinbasef95fbf0c9f2c6f…3adfe9f74efd77
1 in β†’ 1 out8.4600 XPM110 B
AGvRfDpz…1i6rPddM
c9d006d6c8085d…49850824c8f356
8 in β†’ 2 out718.0782 XPM1.23 KB
AM8FWB4X…tuJXovdpAdZQhb7U…6CmgErkj
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.

5.414 Γ— 10⁹⁴(95-digit number)
54147185015381624905…02875477752302662399
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
5.414 Γ— 10⁹⁴(95-digit number)
54147185015381624905…02875477752302662399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁡(96-digit number)
10829437003076324981…05750955504605324799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.165 Γ— 10⁹⁡(96-digit number)
21658874006152649962…11501911009210649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.331 Γ— 10⁹⁡(96-digit number)
43317748012305299924…23003822018421299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.663 Γ— 10⁹⁡(96-digit number)
86635496024610599849…46007644036842598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.732 Γ— 10⁹⁢(97-digit number)
17327099204922119969…92015288073685196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.465 Γ— 10⁹⁢(97-digit number)
34654198409844239939…84030576147370393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.930 Γ— 10⁹⁢(97-digit number)
69308396819688479879…68061152294740787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁷(98-digit number)
13861679363937695975…36122304589481574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.772 Γ— 10⁹⁷(98-digit number)
27723358727875391951…72244609178963148799
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:57,988,537 XPMΒ·at block #6,843,022 Β· updates every 60s
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