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Block #1,138,446

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/3/2015, 4:20:56 PM Β· Difficulty 10.9363 Β· 5,706,577 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6d0dd0986c0f0d5727107044b8c8eb4769d18c840eb42458b6e8e64c57b87383
View on Chainz β†—

Height

#1,138,446

Difficulty

10.936342

Transactions

2

Size

3.60 KB

Version

2

Bits

0aefb417

Nonce

1,474,309,532

Timestamp

7/3/2015, 4:20:56 PM

Confirmations

5,706,577

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

4d636d202a7145a1e4f845baa9b0cc568b562706596c3243f88c8cf6b648d76f
Transactions (2)
Coinbase764e7b273b61e9…0aa673dce25d1d
1 in β†’ 1 out8.3900 XPM116 B
AJCEY9yy…tg97E6zm
58e1a3e21466b0…aea893ac85764f
23 in β†’ 2 out2371.2823 XPM3.40 KB
ANAcA2SL…2tet9jgCAKF62uTm…SVwSSCmN
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.

5.628 Γ— 10⁹⁡(96-digit number)
56287121391630044032…57709620228045923839
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
5.628 Γ— 10⁹⁡(96-digit number)
56287121391630044032…57709620228045923839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁢(97-digit number)
11257424278326008806…15419240456091847679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.251 Γ— 10⁹⁢(97-digit number)
22514848556652017612…30838480912183695359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.502 Γ— 10⁹⁢(97-digit number)
45029697113304035225…61676961824367390719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.005 Γ— 10⁹⁢(97-digit number)
90059394226608070451…23353923648734781439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.801 Γ— 10⁹⁷(98-digit number)
18011878845321614090…46707847297469562879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.602 Γ— 10⁹⁷(98-digit number)
36023757690643228180…93415694594939125759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.204 Γ— 10⁹⁷(98-digit number)
72047515381286456361…86831389189878251519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.440 Γ— 10⁹⁸(99-digit number)
14409503076257291272…73662778379756503039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.881 Γ— 10⁹⁸(99-digit number)
28819006152514582544…47325556759513006079
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:58,004,608 XPMΒ·at block #6,845,022 Β· updates every 60s
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