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Block #2,190,469

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/3/2017, 3:48:04 AM Β· Difficulty 10.9496 Β· 4,636,089 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d9efd109bfad77ae6115b1872cb64c43d47c56eb62d8f8b6196a16fbe92bd02
View on Chainz β†—

Height

#2,190,469

Difficulty

10.949582

Transactions

2

Size

873 B

Version

2

Bits

0af317d0

Nonce

1,594,044,993

Timestamp

7/3/2017, 3:48:04 AM

Confirmations

4,636,089

Mined by

⛏️ P2SHAJ6QGTb2pNh2y8P4A7Q7DhdQRogK1StTm7

Merkle Root

e5c719be3914003ad4541eb8e377b14c5f84de1d1211b61e9bfcbd6e180b9932
Transactions (2)
Coinbase2a78f353e5b1c6…2f60d659c87cdf
1 in β†’ 1 out8.3400 XPM110 B
AJ6QGTb2…gK1StTm7
c54f43bd79105c…598865094c74a3
4 in β†’ 2 out1835.2729 XPM672 B
AKUvJZT8…P77eytzXAdLv38Pf…k1z3e6Dc
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.

8.306 Γ— 10⁹⁡(96-digit number)
83065787100411679885…55696401464526405119
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
8.306 Γ— 10⁹⁡(96-digit number)
83065787100411679885…55696401464526405119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.661 Γ— 10⁹⁢(97-digit number)
16613157420082335977…11392802929052810239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.322 Γ— 10⁹⁢(97-digit number)
33226314840164671954…22785605858105620479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.645 Γ— 10⁹⁢(97-digit number)
66452629680329343908…45571211716211240959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.329 Γ— 10⁹⁷(98-digit number)
13290525936065868781…91142423432422481919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.658 Γ— 10⁹⁷(98-digit number)
26581051872131737563…82284846864844963839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.316 Γ— 10⁹⁷(98-digit number)
53162103744263475126…64569693729689927679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁸(99-digit number)
10632420748852695025…29139387459379855359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.126 Γ— 10⁹⁸(99-digit number)
21264841497705390050…58278774918759710719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.252 Γ— 10⁹⁸(99-digit number)
42529682995410780101…16557549837519421439
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:57,856,615 XPMΒ·at block #6,826,557 Β· updates every 60s
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