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Block #93,735

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/2/2013, 3:34:54 PM Β· Difficulty 9.1949 Β· 6,709,646 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d66900cf20116b50bb0727bc76a7fa5c8c5f639abc60f7d7b68bd6003a13769b
View on Chainz β†—

Height

#93,735

Difficulty

9.194897

Transactions

2

Size

869 B

Version

2

Bits

0931e4cd

Nonce

409,600

Timestamp

8/2/2013, 3:34:54 PM

Confirmations

6,709,646

Mined by

⛏️ P2SHAMDB4YMnXanoPZX8YQhHrS6PenPSPoU5gY

Merkle Root

92007879269c787975c08532db617a7e62c72b23f0de83b066476cbc5bae0629
Transactions (2)
Coinbase58418077f2bc65…29a980c2284edd
1 in β†’ 1 out11.8200 XPM109 B
AMDB4YMn…PSPoU5gY
55632535d1c287…46a674672876e7
4 in β†’ 2 out400.0117 XPM670 B
AXqYmuZz…cAX62EgCAPMGbH5f…JG5Qga2G
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.

3.204 Γ— 10⁹³(94-digit number)
32046067591286634670…88007714650003630699
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
3.204 Γ— 10⁹³(94-digit number)
32046067591286634670…88007714650003630699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.409 Γ— 10⁹³(94-digit number)
64092135182573269340…76015429300007261399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.281 Γ— 10⁹⁴(95-digit number)
12818427036514653868…52030858600014522799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.563 Γ— 10⁹⁴(95-digit number)
25636854073029307736…04061717200029045599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.127 Γ— 10⁹⁴(95-digit number)
51273708146058615472…08123434400058091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁡(96-digit number)
10254741629211723094…16246868800116182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.050 Γ— 10⁹⁡(96-digit number)
20509483258423446188…32493737600232364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.101 Γ— 10⁹⁡(96-digit number)
41018966516846892377…64987475200464729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.203 Γ— 10⁹⁡(96-digit number)
82037933033693784755…29974950400929459199
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:57,671,085 XPMΒ·at block #6,803,380 Β· updates every 60s
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