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Block #2,913,174

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/7/2018, 3:23:19 AM Β· Difficulty 11.4985 Β· 3,919,833 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be7f762e460b699aeaf657e0627967024c84463bd31b501c19408c923bd50e99
View on Chainz β†—

Height

#2,913,174

Difficulty

11.498543

Transactions

2

Size

390 B

Version

2

Bits

0b7fa086

Nonce

590,336,653

Timestamp

11/7/2018, 3:23:19 AM

Confirmations

3,919,833

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

efa6b1295add3fe50b4c99d5678540f37918bafde64c13a98332bac5b05b66b9
Transactions (2)
Coinbaseb1063d55c64248…4fc4892b3ba45f
1 in β†’ 1 out7.5600 XPM109 B
AUMQRepm…tAfKmdW1
472522229f7451…8f323656ac933d
1 in β†’ 1 out178.6809 XPM191 B
AbFieDh2…UG9e4SDN
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.

5.595 Γ— 10⁹³(94-digit number)
55954555294438230131…46767745238182850659
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
5.595 Γ— 10⁹³(94-digit number)
55954555294438230131…46767745238182850659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.119 Γ— 10⁹⁴(95-digit number)
11190911058887646026…93535490476365701319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.238 Γ— 10⁹⁴(95-digit number)
22381822117775292052…87070980952731402639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.476 Γ— 10⁹⁴(95-digit number)
44763644235550584105…74141961905462805279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.952 Γ— 10⁹⁴(95-digit number)
89527288471101168210…48283923810925610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.790 Γ— 10⁹⁡(96-digit number)
17905457694220233642…96567847621851221119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.581 Γ— 10⁹⁡(96-digit number)
35810915388440467284…93135695243702442239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.162 Γ— 10⁹⁡(96-digit number)
71621830776880934568…86271390487404884479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁢(97-digit number)
14324366155376186913…72542780974809768959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.864 Γ— 10⁹⁢(97-digit number)
28648732310752373827…45085561949619537919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.729 Γ— 10⁹⁢(97-digit number)
57297464621504747654…90171123899239075839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,908,230 XPMΒ·at block #6,833,006 Β· updates every 60s
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