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Block #3,056,763

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/17/2019, 11:33:37 AM Β· Difficulty 11.0082 Β· 3,781,646 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
abe5982d10d293b479446feceecbb8b2e0e56d49a97679486f8bdca9a999acff
View on Chainz β†—

Height

#3,056,763

Difficulty

11.008198

Transactions

2

Size

723 B

Version

2

Bits

0b021948

Nonce

810,406,314

Timestamp

2/17/2019, 11:33:37 AM

Confirmations

3,781,646

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

a84151b0207e60391a00dbfc2867e1ec4c8e8914665fff6cf99e763ebecd9155
Transactions (2)
Coinbase66ca0a11e3a1ca…19d6ce207bf529
1 in β†’ 1 out8.2500 XPM110 B
AUhjokok…k5m93PZR
d8f604b9128303…13089f04786c16
3 in β†’ 2 out4.2910 XPM522 B
AeTHTL7A…vT1872bkAQdp3a9z…VAi7pgSt
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.

1.667 Γ— 10⁹⁷(98-digit number)
16679616568824429439…68177040097803765759
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
1.667 Γ— 10⁹⁷(98-digit number)
16679616568824429439…68177040097803765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.335 Γ— 10⁹⁷(98-digit number)
33359233137648858878…36354080195607531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.671 Γ— 10⁹⁷(98-digit number)
66718466275297717756…72708160391215063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁸(99-digit number)
13343693255059543551…45416320782430126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.668 Γ— 10⁹⁸(99-digit number)
26687386510119087102…90832641564860252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.337 Γ— 10⁹⁸(99-digit number)
53374773020238174204…81665283129720504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁹(100-digit number)
10674954604047634840…63330566259441008639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.134 Γ— 10⁹⁹(100-digit number)
21349909208095269681…26661132518882017279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.269 Γ— 10⁹⁹(100-digit number)
42699818416190539363…53322265037764034559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.539 Γ— 10⁹⁹(100-digit number)
85399636832381078727…06644530075528069119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.707 Γ— 10¹⁰⁰(101-digit number)
17079927366476215745…13289060151056138239
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:57,951,544 XPMΒ·at block #6,838,408 Β· updates every 60s
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