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Block #1,407,562

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/10/2016, 5:17:36 PM Β· Difficulty 10.8047 Β· 5,397,441 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
801ff3f3a7e6dc2f1ab7ffed434184787422a0a85b1b0e8127ebc3e93686de39
View on Chainz β†—

Height

#1,407,562

Difficulty

10.804717

Transactions

2

Size

5.77 KB

Version

2

Bits

0ace01ea

Nonce

522,852,936

Timestamp

1/10/2016, 5:17:36 PM

Confirmations

5,397,441

Mined by

⛏️ P2SHATZtX1nsKEP6Gppy6YSnSqRVWCyjRbcK8L

Merkle Root

da717792cc6bfcc43c40c6b41daceb1c90a282fb2779f1a61fc080af0e317d24
Transactions (2)
Coinbase58b177a41c80ba…283c5b707c647e
1 in β†’ 1 out8.6200 XPM109 B
ATZtX1ns…yjRbcK8L
55544100614f4f…59afe891f858c7
38 in β†’ 2 out76.9533 XPM5.57 KB
AGky5ni4…jnaoQ88PANg9dMxk…e3wX2ZW4
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.

1.321 Γ— 10⁹⁢(97-digit number)
13211220605306657753…67730310224443130879
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
1.321 Γ— 10⁹⁢(97-digit number)
13211220605306657753…67730310224443130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.642 Γ— 10⁹⁢(97-digit number)
26422441210613315507…35460620448886261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.284 Γ— 10⁹⁢(97-digit number)
52844882421226631014…70921240897772523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.056 Γ— 10⁹⁷(98-digit number)
10568976484245326202…41842481795545047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.113 Γ— 10⁹⁷(98-digit number)
21137952968490652405…83684963591090094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.227 Γ— 10⁹⁷(98-digit number)
42275905936981304811…67369927182180188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.455 Γ— 10⁹⁷(98-digit number)
84551811873962609622…34739854364360376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.691 Γ— 10⁹⁸(99-digit number)
16910362374792521924…69479708728720752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.382 Γ— 10⁹⁸(99-digit number)
33820724749585043849…38959417457441505279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.764 Γ— 10⁹⁸(99-digit number)
67641449499170087698…77918834914883010559
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:57,684,095 XPMΒ·at block #6,805,002 Β· updates every 60s
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