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Block #1,132,018

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/29/2015, 7:08:57 AM Β· Difficulty 10.9346 Β· 5,681,001 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c60393c0f6d638befb62364b23dbd0f80202efe69feeb538389c22fd0fa5c113
View on Chainz β†—

Height

#1,132,018

Difficulty

10.934648

Transactions

2

Size

1.57 KB

Version

2

Bits

0aef4517

Nonce

395,159,468

Timestamp

6/29/2015, 7:08:57 AM

Confirmations

5,681,001

Mined by

⛏️ P2SHAGmMJ3Cn6MpvfpBw82nJxUDTXnPA1N8aYb

Merkle Root

2601c677d63c6bfa5c4f417a987dad141cce6dbb63064e02b5cc4e4cee0df0c7
Transactions (2)
Coinbaseed8c66e3ae37a1…22273bbcd5405c
1 in β†’ 1 out8.3700 XPM110 B
AGmMJ3Cn…PA1N8aYb
6abc62ea5d19b1…74079955beba8b
9 in β†’ 2 out42.5426 XPM1.38 KB
AK9LxQQh…h24pctRmATh3Q3XC…AVpA1dTJ
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.

6.717 Γ— 10⁹⁴(95-digit number)
67172372222402194705…58181990167137701239
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
6.717 Γ— 10⁹⁴(95-digit number)
67172372222402194705…58181990167137701239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁡(96-digit number)
13434474444480438941…16363980334275402479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.686 Γ— 10⁹⁡(96-digit number)
26868948888960877882…32727960668550804959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.373 Γ— 10⁹⁡(96-digit number)
53737897777921755764…65455921337101609919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁢(97-digit number)
10747579555584351152…30911842674203219839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁢(97-digit number)
21495159111168702305…61823685348406439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.299 Γ— 10⁹⁢(97-digit number)
42990318222337404611…23647370696812879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.598 Γ— 10⁹⁢(97-digit number)
85980636444674809222…47294741393625758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁷(98-digit number)
17196127288934961844…94589482787251517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.439 Γ— 10⁹⁷(98-digit number)
34392254577869923688…89178965574503034879
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:57,748,193 XPMΒ·at block #6,813,018 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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