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Block #2,287,971

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2017, 3:18:53 PM Β· Difficulty 10.9555 Β· 4,552,948 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
01240c697369a5e7fb9e978569c306534768374f42c2bcfba9480e06392a4831
View on Chainz β†—

Height

#2,287,971

Difficulty

10.955479

Transactions

2

Size

426 B

Version

2

Bits

0af49a40

Nonce

495,325,923

Timestamp

9/8/2017, 3:18:53 PM

Confirmations

4,552,948

Mined by

⛏️ P2SHAcwo5ZkM6sXhHkGigZwQaca1GtT1KUFApZ

Merkle Root

f4be7d074e4ad59825ad91a4cbfeb98b628197ff0e55fc22ee0b3e17dc4f9b4b
Transactions (2)
Coinbase5e8183660efdad…08f9efa7df335b
1 in β†’ 1 out8.3300 XPM110 B
Acwo5ZkM…T1KUFApZ
3af6f3bea77fc5…43f03a3cbd3a81
1 in β†’ 2 out2937.1235 XPM226 B
AViBaKwf…3Xk3qwK8AWwKmAp2…v5Tdwytm
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.

2.714 Γ— 10⁹⁴(95-digit number)
27144716272476697297…33925086904896975439
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
2.714 Γ— 10⁹⁴(95-digit number)
27144716272476697297…33925086904896975439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.428 Γ— 10⁹⁴(95-digit number)
54289432544953394595…67850173809793950879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.085 Γ— 10⁹⁡(96-digit number)
10857886508990678919…35700347619587901759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.171 Γ— 10⁹⁡(96-digit number)
21715773017981357838…71400695239175803519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.343 Γ— 10⁹⁡(96-digit number)
43431546035962715676…42801390478351607039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.686 Γ— 10⁹⁡(96-digit number)
86863092071925431353…85602780956703214079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.737 Γ— 10⁹⁢(97-digit number)
17372618414385086270…71205561913406428159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.474 Γ— 10⁹⁢(97-digit number)
34745236828770172541…42411123826812856319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.949 Γ— 10⁹⁢(97-digit number)
69490473657540345082…84822247653625712639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.389 Γ— 10⁹⁷(98-digit number)
13898094731508069016…69644495307251425279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.779 Γ— 10⁹⁷(98-digit number)
27796189463016138033…39288990614502850559
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:57,971,703 XPMΒ·at block #6,840,918 Β· updates every 60s
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