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Block #1,924,534

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/5/2017, 5:11:26 AM Β· Difficulty 10.7220 Β· 4,916,520 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f7eeda0b3afbda98b8463643bc741732865d8426351d716d4ef5b2a4b2ad1fac
View on Chainz β†—

Height

#1,924,534

Difficulty

10.721979

Transactions

1

Size

201 B

Version

2

Bits

0ab8d3a2

Nonce

485,207,307

Timestamp

1/5/2017, 5:11:26 AM

Confirmations

4,916,520

Mined by

⛏️ P2SHAMwxkGUeKVTTjBdvfHaF1zBZd7uJTm8sgW

Merkle Root

7f0881036686af7a531187c4ed59e2b23b6bdd48240c3f1236ccd9cf1a8d25ee
Transactions (1)
Coinbase7f0881036686af…ccd9cf1a8d25ee
1 in β†’ 1 out8.6800 XPM110 B
AMwxkGUe…uJTm8sgW
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.

8.636 Γ— 10⁹⁡(96-digit number)
86369362677176274501…47553957657444613119
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
8.636 Γ— 10⁹⁡(96-digit number)
86369362677176274501…47553957657444613119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁢(97-digit number)
17273872535435254900…95107915314889226239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.454 Γ— 10⁹⁢(97-digit number)
34547745070870509800…90215830629778452479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.909 Γ— 10⁹⁢(97-digit number)
69095490141741019601…80431661259556904959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.381 Γ— 10⁹⁷(98-digit number)
13819098028348203920…60863322519113809919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.763 Γ— 10⁹⁷(98-digit number)
27638196056696407840…21726645038227619839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.527 Γ— 10⁹⁷(98-digit number)
55276392113392815681…43453290076455239679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.105 Γ— 10⁹⁸(99-digit number)
11055278422678563136…86906580152910479359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.211 Γ— 10⁹⁸(99-digit number)
22110556845357126272…73813160305820958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.422 Γ— 10⁹⁸(99-digit number)
44221113690714252544…47626320611641917439
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:57,972,795 XPMΒ·at block #6,841,053 Β· updates every 60s
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