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Block #1,562,494

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2016, 11:37:09 AM Β· Difficulty 10.7329 Β· 5,271,408 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
71cddb933f69fa385bbbd895aaa4afbe19f1c4d29fc7fefa985371a30594da86
View on Chainz β†—

Height

#1,562,494

Difficulty

10.732915

Transactions

2

Size

834 B

Version

2

Bits

0abba04e

Nonce

361,500,376

Timestamp

4/28/2016, 11:37:09 AM

Confirmations

5,271,408

Mined by

⛏️ P2SHANyEc2sjyMvpwsABhEicCb4oF64edE8Jme

Merkle Root

19ec9d6afa83fde556da398e2834e8d5eeb3b4595a3c799ca862b8fa0f4a7d36
Transactions (2)
Coinbase5c99d79adcaca3…3ae6038e9a4879
1 in β†’ 1 out8.6800 XPM109 B
ANyEc2sj…4edE8Jme
d5b28099c0b31f…b8ff8bff96c8d7
4 in β†’ 1 out10178.0000 XPM635 B
AJ1W4Wt6…cSqw2yEm
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.

2.519 Γ— 10⁹³(94-digit number)
25191856761875335980…78817494756353743359
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
2.519 Γ— 10⁹³(94-digit number)
25191856761875335980…78817494756353743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.038 Γ— 10⁹³(94-digit number)
50383713523750671961…57634989512707486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁴(95-digit number)
10076742704750134392…15269979025414973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.015 Γ— 10⁹⁴(95-digit number)
20153485409500268784…30539958050829946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.030 Γ— 10⁹⁴(95-digit number)
40306970819000537568…61079916101659893759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.061 Γ— 10⁹⁴(95-digit number)
80613941638001075137…22159832203319787519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁡(96-digit number)
16122788327600215027…44319664406639575039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁡(96-digit number)
32245576655200430055…88639328813279150079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.449 Γ— 10⁹⁡(96-digit number)
64491153310400860110…77278657626558300159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.289 Γ— 10⁹⁢(97-digit number)
12898230662080172022…54557315253116600319
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:57,915,442 XPMΒ·at block #6,833,901 Β· updates every 60s
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