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Block #2,234,587

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/3/2017, 3:29:36 AM Β· Difficulty 10.9457 Β· 4,605,530 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa9007d27e031373e1a5e064260e251fe2bd642496171e7e8e9bd326ab7458cc
View on Chainz β†—

Height

#2,234,587

Difficulty

10.945684

Transactions

2

Size

720 B

Version

2

Bits

0af2185e

Nonce

1,111,073,297

Timestamp

8/3/2017, 3:29:36 AM

Confirmations

4,605,530

Mined by

⛏️ P2SHAReGbLLFyy4SjYqqAwk6D8B2EbfR5rSoGu

Merkle Root

bc4808cfd8cbe8d56b6677fb3f8bfc742bd2d81130946b3fa8c73c6e7d7f6391
Transactions (2)
Coinbase258e9bb186345a…40c92a02527ffa
1 in β†’ 1 out8.3400 XPM109 B
AReGbLLF…fR5rSoGu
1acf78d844724d…2c8df9b6228c39
3 in β†’ 2 out1484.0302 XPM521 B
AWRDnK93…19VviqfzAc1vXGDf…kpUgZCtL
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.

1.289 Γ— 10⁹⁴(95-digit number)
12893010474347537516…80848153139384847369
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
1.289 Γ— 10⁹⁴(95-digit number)
12893010474347537516…80848153139384847369
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.578 Γ— 10⁹⁴(95-digit number)
25786020948695075032…61696306278769694739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.157 Γ— 10⁹⁴(95-digit number)
51572041897390150065…23392612557539389479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁡(96-digit number)
10314408379478030013…46785225115078778959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.062 Γ— 10⁹⁡(96-digit number)
20628816758956060026…93570450230157557919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.125 Γ— 10⁹⁡(96-digit number)
41257633517912120052…87140900460315115839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.251 Γ— 10⁹⁡(96-digit number)
82515267035824240104…74281800920630231679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.650 Γ— 10⁹⁢(97-digit number)
16503053407164848020…48563601841260463359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.300 Γ— 10⁹⁢(97-digit number)
33006106814329696041…97127203682520926719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.601 Γ— 10⁹⁢(97-digit number)
66012213628659392083…94254407365041853439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.320 Γ— 10⁹⁷(98-digit number)
13202442725731878416…88508814730083706879
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:57,965,248 XPMΒ·at block #6,840,116 Β· updates every 60s
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