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Block #2,270,334

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2017, 1:17:24 PM Β· Difficulty 10.9528 Β· 4,572,765 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2637774104388bd4c2ad87acb3d9213ad86eea002b9535cbdf16d46d325f38b4
View on Chainz β†—

Height

#2,270,334

Difficulty

10.952781

Transactions

1

Size

200 B

Version

2

Bits

0af3e979

Nonce

280,380,946

Timestamp

8/27/2017, 1:17:24 PM

Confirmations

4,572,765

Mined by

⛏️ P2SHAKwq71oGy75BjdSwmLtiK9WNUU4iPLuBDH

Merkle Root

b3a56149ec4f07ece94edafb2778b4cd913314fcfa4b26caa0c140066a86f995
Transactions (1)
Coinbaseb3a56149ec4f07…c140066a86f995
1 in β†’ 1 out8.3200 XPM110 B
AKwq71oG…4iPLuBDH
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.

4.221 Γ— 10⁹⁴(95-digit number)
42211933659514288721…04309844539316518359
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
4.221 Γ— 10⁹⁴(95-digit number)
42211933659514288721…04309844539316518359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.442 Γ— 10⁹⁴(95-digit number)
84423867319028577442…08619689078633036719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.688 Γ— 10⁹⁡(96-digit number)
16884773463805715488…17239378157266073439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.376 Γ— 10⁹⁡(96-digit number)
33769546927611430977…34478756314532146879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.753 Γ— 10⁹⁡(96-digit number)
67539093855222861954…68957512629064293759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.350 Γ— 10⁹⁢(97-digit number)
13507818771044572390…37915025258128587519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.701 Γ— 10⁹⁢(97-digit number)
27015637542089144781…75830050516257175039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.403 Γ— 10⁹⁢(97-digit number)
54031275084178289563…51660101032514350079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁷(98-digit number)
10806255016835657912…03320202065028700159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.161 Γ— 10⁹⁷(98-digit number)
21612510033671315825…06640404130057400319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.322 Γ— 10⁹⁷(98-digit number)
43225020067342631650…13280808260114800639
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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