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Block #223,861

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/23/2013, 8:32:42 AM Β· Difficulty 9.9374 Β· 6,576,806 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
35e17c3ee0def8d9abfac721e829e720b292e42467ed193ee44ff3208cc32359
View on Chainz β†—

Height

#223,861

Difficulty

9.937404

Transactions

1

Size

199 B

Version

2

Bits

09eff9b2

Nonce

164,874

Timestamp

10/23/2013, 8:32:42 AM

Confirmations

6,576,806

Mined by

⛏️ P2SHAKBLmV17J18xdhFa9FnD3pYPLotVhtRsKQ

Merkle Root

6ffc1dfe9d527157469b8f832d7050ffc3194e4d8d4b68e42ab71ef5e4a02ad3
Transactions (1)
Coinbase6ffc1dfe9d5271…b71ef5e4a02ad3
1 in β†’ 1 out10.1100 XPM109 B
AKBLmV17…tVhtRsKQ
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.

1.582 Γ— 10⁹⁴(95-digit number)
15824567325186919765…69260996229420298879
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
1.582 Γ— 10⁹⁴(95-digit number)
15824567325186919765…69260996229420298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.164 Γ— 10⁹⁴(95-digit number)
31649134650373839531…38521992458840597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.329 Γ— 10⁹⁴(95-digit number)
63298269300747679062…77043984917681195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.265 Γ— 10⁹⁡(96-digit number)
12659653860149535812…54087969835362391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.531 Γ— 10⁹⁡(96-digit number)
25319307720299071625…08175939670724782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.063 Γ— 10⁹⁡(96-digit number)
50638615440598143250…16351879341449564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.012 Γ— 10⁹⁢(97-digit number)
10127723088119628650…32703758682899128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.025 Γ— 10⁹⁢(97-digit number)
20255446176239257300…65407517365798256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.051 Γ— 10⁹⁢(97-digit number)
40510892352478514600…30815034731596513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.102 Γ— 10⁹⁢(97-digit number)
81021784704957029200…61630069463193026559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,649,399 XPMΒ·at block #6,800,666 Β· updates every 60s
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