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Block #97,184

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/4/2013, 2:18:38 PM Β· Difficulty 9.2964 Β· 6,710,767 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f62bf2aebdd15d5e06e46d3dfc72e495bfb39c9e461e09f2ab2319899a5dad2
View on Chainz β†—

Height

#97,184

Difficulty

9.296408

Transactions

1

Size

199 B

Version

2

Bits

094be167

Nonce

613,148

Timestamp

8/4/2013, 2:18:38 PM

Confirmations

6,710,767

Mined by

⛏️ P2SHAezMwyLP2hpT3yh3LDZkydqkpsrTg7Eyfk

Merkle Root

758295e2b75e6372782279e8463142d780e325bd1dabff23aa3a97c6689c3b78
Transactions (1)
Coinbase758295e2b75e63…3a97c6689c3b78
1 in β†’ 1 out11.5500 XPM109 B
AezMwyLP…rTg7Eyfk
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.

1.747 Γ— 10⁹⁡(96-digit number)
17474387250208658120…60061552079030052269
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
1.747 Γ— 10⁹⁡(96-digit number)
17474387250208658120…60061552079030052269
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.494 Γ— 10⁹⁡(96-digit number)
34948774500417316241…20123104158060104539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.989 Γ— 10⁹⁡(96-digit number)
69897549000834632483…40246208316120209079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.397 Γ— 10⁹⁢(97-digit number)
13979509800166926496…80492416632240418159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.795 Γ— 10⁹⁢(97-digit number)
27959019600333852993…60984833264480836319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.591 Γ— 10⁹⁢(97-digit number)
55918039200667705987…21969666528961672639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁷(98-digit number)
11183607840133541197…43939333057923345279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.236 Γ— 10⁹⁷(98-digit number)
22367215680267082394…87878666115846690559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.473 Γ— 10⁹⁷(98-digit number)
44734431360534164789…75757332231693381119
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:57,707,649 XPMΒ·at block #6,807,950 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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