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Block #2,640,103

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 9:24:47 PM Β· Difficulty 11.5670 Β· 4,201,906 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aae0827a5fe4a64256327621aedaeed15ef4ebf911b6e73fee71cc2187185993
View on Chainz β†—

Height

#2,640,103

Difficulty

11.566993

Transactions

1

Size

200 B

Version

2

Bits

0b91266c

Nonce

665,581,483

Timestamp

4/30/2018, 9:24:47 PM

Confirmations

4,201,906

Mined by

⛏️ P2SHAcfcENLqbeAzZj72JneJKtrBfAgvWPw9nH

Merkle Root

fac5a48b1efe7042e2d1148ed3016075339ed3e986e1709498a26d87a8fe26e3
Transactions (1)
Coinbasefac5a48b1efe70…a26d87a8fe26e3
1 in β†’ 1 out7.4600 XPM110 B
AcfcENLq…gvWPw9nH
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.

8.530 Γ— 10⁹⁴(95-digit number)
85306087702174057590…75786616611907420159
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
8.530 Γ— 10⁹⁴(95-digit number)
85306087702174057590…75786616611907420159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.706 Γ— 10⁹⁡(96-digit number)
17061217540434811518…51573233223814840319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.412 Γ— 10⁹⁡(96-digit number)
34122435080869623036…03146466447629680639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.824 Γ— 10⁹⁡(96-digit number)
68244870161739246072…06292932895259361279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.364 Γ— 10⁹⁢(97-digit number)
13648974032347849214…12585865790518722559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.729 Γ— 10⁹⁢(97-digit number)
27297948064695698429…25171731581037445119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.459 Γ— 10⁹⁢(97-digit number)
54595896129391396858…50343463162074890239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁷(98-digit number)
10919179225878279371…00686926324149780479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.183 Γ— 10⁹⁷(98-digit number)
21838358451756558743…01373852648299560959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.367 Γ— 10⁹⁷(98-digit number)
43676716903513117486…02747705296599121919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.735 Γ— 10⁹⁷(98-digit number)
87353433807026234972…05495410593198243839
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
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