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Block #186,636

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/30/2013, 12:34:45 AM Β· Difficulty 9.8671 Β· 6,608,700 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
517b5858d9328cc786a64d62f4cbb476886a714386ac9341d3c06cddcc167a88
View on Chainz β†—

Height

#186,636

Difficulty

9.867108

Transactions

2

Size

357 B

Version

2

Bits

09ddfad1

Nonce

57,119

Timestamp

9/30/2013, 12:34:45 AM

Confirmations

6,608,700

Mined by

⛏️ P2SHAYU29pAMTGTwdxXig1rNVPZQVoBQD1vpUA

Merkle Root

1302901c768d496282852355691ce6f91638f9ecbaabde1e5f869e2d6fe80ff5
Transactions (2)
Coinbase9b98c643f6b9c4…8d4130eafb58e3
1 in β†’ 1 out10.2700 XPM109 B
AYU29pAM…BQD1vpUA
6f269cd2a0a8cf…912b8259b1c313
1 in β†’ 1 out10.2800 XPM158 B
Ad4tU5FR…YoLG8ved
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.

1.562 Γ— 10⁹⁴(95-digit number)
15626316377544224511…86361385138733986239
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
1.562 Γ— 10⁹⁴(95-digit number)
15626316377544224511…86361385138733986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.125 Γ— 10⁹⁴(95-digit number)
31252632755088449023…72722770277467972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.250 Γ— 10⁹⁴(95-digit number)
62505265510176898046…45445540554935944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁡(96-digit number)
12501053102035379609…90891081109871889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.500 Γ— 10⁹⁡(96-digit number)
25002106204070759218…81782162219743779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.000 Γ— 10⁹⁡(96-digit number)
50004212408141518437…63564324439487559679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁢(97-digit number)
10000842481628303687…27128648878975119359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.000 Γ— 10⁹⁢(97-digit number)
20001684963256607374…54257297757950238719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.000 Γ— 10⁹⁢(97-digit number)
40003369926513214749…08514595515900477439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,606,746 XPMΒ·at block #6,795,335 Β· updates every 60s
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