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Block #1,613,450

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/4/2016, 7:31:57 AM Β· Difficulty 10.5991 Β· 5,227,945 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55ebf74069de1221fe9cdca157fe5a7461f263c46425d2b0b2cd4d2266cfeffb
View on Chainz β†—

Height

#1,613,450

Difficulty

10.599074

Transactions

1

Size

199 B

Version

2

Bits

0a995ce5

Nonce

763,365,883

Timestamp

6/4/2016, 7:31:57 AM

Confirmations

5,227,945

Mined by

⛏️ P2SHAHRA7ougQxcu4W2ToDMwtmzuQwgxb9aqR8

Merkle Root

2889167a992a94d30fc030df6f84525beecfcd9a47201038a5bf9ae13465c528
Transactions (1)
Coinbase2889167a992a94…bf9ae13465c528
1 in β†’ 1 out8.8900 XPM109 B
AHRA7oug…gxb9aqR8
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.

1.269 Γ— 10⁹⁡(96-digit number)
12694210961986886262…58918553979033191279
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
1.269 Γ— 10⁹⁡(96-digit number)
12694210961986886262…58918553979033191279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.538 Γ— 10⁹⁡(96-digit number)
25388421923973772525…17837107958066382559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.077 Γ— 10⁹⁡(96-digit number)
50776843847947545051…35674215916132765119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁢(97-digit number)
10155368769589509010…71348431832265530239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.031 Γ— 10⁹⁢(97-digit number)
20310737539179018020…42696863664531060479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.062 Γ— 10⁹⁢(97-digit number)
40621475078358036041…85393727329062120959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.124 Γ— 10⁹⁢(97-digit number)
81242950156716072082…70787454658124241919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.624 Γ— 10⁹⁷(98-digit number)
16248590031343214416…41574909316248483839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.249 Γ— 10⁹⁷(98-digit number)
32497180062686428832…83149818632496967679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.499 Γ— 10⁹⁷(98-digit number)
64994360125372857665…66299637264993935359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁸(99-digit number)
12998872025074571533…32599274529987870719
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:57,975,532 XPMΒ·at block #6,841,394 Β· updates every 60s
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