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Block #2,788,619

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/11/2018, 2:17:40 AM Β· Difficulty 11.6734 Β· 4,051,325 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e8a06017e184c307bd61fea3fae3e7d1643c36d2712259bd5b42e1ed9977ffdc
View on Chainz β†—

Height

#2,788,619

Difficulty

11.673393

Transactions

1

Size

199 B

Version

2

Bits

0bac637a

Nonce

26,336,890

Timestamp

8/11/2018, 2:17:40 AM

Confirmations

4,051,325

Mined by

⛏️ P2SHAUUntTcjAzyiJGGudXT8sDXvHLvVHoDLbB

Merkle Root

b9965eea80827b6390d89c7c184f1e5405fe01b4c7eeb9d8ff9f796478cf641f
Transactions (1)
Coinbaseb9965eea80827b…9f796478cf641f
1 in β†’ 1 out7.3300 XPM109 B
AUUntTcj…vVHoDLbB
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.

2.672 Γ— 10⁹⁡(96-digit number)
26725222861822298181…14873370967616227839
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
2.672 Γ— 10⁹⁡(96-digit number)
26725222861822298181…14873370967616227839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.345 Γ— 10⁹⁡(96-digit number)
53450445723644596363…29746741935232455679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁢(97-digit number)
10690089144728919272…59493483870464911359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.138 Γ— 10⁹⁢(97-digit number)
21380178289457838545…18986967740929822719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.276 Γ— 10⁹⁢(97-digit number)
42760356578915677090…37973935481859645439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.552 Γ— 10⁹⁢(97-digit number)
85520713157831354181…75947870963719290879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.710 Γ— 10⁹⁷(98-digit number)
17104142631566270836…51895741927438581759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.420 Γ— 10⁹⁷(98-digit number)
34208285263132541672…03791483854877163519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.841 Γ— 10⁹⁷(98-digit number)
68416570526265083345…07582967709754327039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.368 Γ— 10⁹⁸(99-digit number)
13683314105253016669…15165935419508654079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.736 Γ— 10⁹⁸(99-digit number)
27366628210506033338…30331870839017308159
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:57,963,852 XPMΒ·at block #6,839,943 Β· updates every 60s
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