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Block #2,644,007

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 7:45:53 AM Β· Difficulty 11.6997 Β· 4,188,456 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c550cbeb6f4c6ce5394d262cdae5607a3b0264f496f3c8ac2215f21e51ab984
View on Chainz β†—

Height

#2,644,007

Difficulty

11.699716

Transactions

1

Size

200 B

Version

2

Bits

0bb32099

Nonce

222,252,078

Timestamp

5/2/2018, 7:45:53 AM

Confirmations

4,188,456

Mined by

⛏️ P2SHAbkpUmsUEMXMFqJ7m5P7N6degHn1PUxd6L

Merkle Root

646beaadd7f0286553d9ece7c407447adfd2b4d73af43459ab895c80f795c2bf
Transactions (1)
Coinbase646beaadd7f028…895c80f795c2bf
1 in β†’ 1 out7.2900 XPM110 B
AbkpUmsU…n1PUxd6L
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.

4.074 Γ— 10⁹³(94-digit number)
40745280258500811100…87130598396504931059
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
4.074 Γ— 10⁹³(94-digit number)
40745280258500811100…87130598396504931059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.149 Γ— 10⁹³(94-digit number)
81490560517001622200…74261196793009862119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.629 Γ— 10⁹⁴(95-digit number)
16298112103400324440…48522393586019724239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.259 Γ— 10⁹⁴(95-digit number)
32596224206800648880…97044787172039448479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.519 Γ— 10⁹⁴(95-digit number)
65192448413601297760…94089574344078896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.303 Γ— 10⁹⁡(96-digit number)
13038489682720259552…88179148688157793919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.607 Γ— 10⁹⁡(96-digit number)
26076979365440519104…76358297376315587839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.215 Γ— 10⁹⁡(96-digit number)
52153958730881038208…52716594752631175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁢(97-digit number)
10430791746176207641…05433189505262351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.086 Γ— 10⁹⁢(97-digit number)
20861583492352415283…10866379010524702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.172 Γ— 10⁹⁢(97-digit number)
41723166984704830566…21732758021049405439
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:57,903,854 XPMΒ·at block #6,832,462 Β· updates every 60s
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