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Block #73,798

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 7:51:54 AM Β· Difficulty 8.9951 Β· 6,730,212 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dbbe665cf6b7ffc82c1de57dc4af74eb5af375012d09e05ce523f4a30a06b0b5
View on Chainz β†—

Height

#73,798

Difficulty

8.995073

Transactions

1

Size

204 B

Version

2

Bits

08febd15

Nonce

227

Timestamp

7/21/2013, 7:51:54 AM

Confirmations

6,730,212

Mined by

⛏️ P2SHAeVvGUh4cnFPF4FMDsxtGiaqQhkYpQ2wDQ

Merkle Root

6fdad1af3cbc037e480f29cb09490753595cff773e6ea5ff049415f4fa3e2db4
Transactions (1)
Coinbase6fdad1af3cbc03…9415f4fa3e2db4
1 in β†’ 1 out12.3400 XPM110 B
AeVvGUh4…kYpQ2wDQ
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.

1.988 Γ— 10¹⁰³(104-digit number)
19885623487480344497…07848962550139153759
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
1.988 Γ— 10¹⁰³(104-digit number)
19885623487480344497…07848962550139153759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.977 Γ— 10¹⁰³(104-digit number)
39771246974960688995…15697925100278307519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.954 Γ— 10¹⁰³(104-digit number)
79542493949921377991…31395850200556615039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.590 Γ— 10¹⁰⁴(105-digit number)
15908498789984275598…62791700401113230079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.181 Γ— 10¹⁰⁴(105-digit number)
31816997579968551196…25583400802226460159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.363 Γ— 10¹⁰⁴(105-digit number)
63633995159937102392…51166801604452920319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.272 Γ— 10¹⁰⁡(106-digit number)
12726799031987420478…02333603208905840639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.545 Γ— 10¹⁰⁡(106-digit number)
25453598063974840957…04667206417811681279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.090 Γ— 10¹⁰⁡(106-digit number)
50907196127949681914…09334412835623362559
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:57,676,128 XPMΒ·at block #6,804,009 Β· updates every 60s
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