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Block #74,616

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 12:04:09 PM Β· Difficulty 8.9956 Β· 6,724,531 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e7dedf89386996654613f47646b97173cfe22005d9fbbd2f7f182095e905e830
View on Chainz β†—

Height

#74,616

Difficulty

8.995619

Transactions

1

Size

199 B

Version

2

Bits

08fee0e4

Nonce

723

Timestamp

7/21/2013, 12:04:09 PM

Confirmations

6,724,531

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

be68ea84dd5ba810e18fa8feaf30243cb944de58dc7cf134b737db22e3a4f83d
Transactions (1)
Coinbasebe68ea84dd5ba8…37db22e3a4f83d
1 in β†’ 1 out12.3400 XPM110 B
ANey87HK…MGUx5bYr
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.

1.468 Γ— 10⁹³(94-digit number)
14681181591901200276…76768147356155030979
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
1.468 Γ— 10⁹³(94-digit number)
14681181591901200276…76768147356155030979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.936 Γ— 10⁹³(94-digit number)
29362363183802400553…53536294712310061959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.872 Γ— 10⁹³(94-digit number)
58724726367604801106…07072589424620123919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.174 Γ— 10⁹⁴(95-digit number)
11744945273520960221…14145178849240247839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.348 Γ— 10⁹⁴(95-digit number)
23489890547041920442…28290357698480495679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.697 Γ— 10⁹⁴(95-digit number)
46979781094083840885…56580715396960991359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.395 Γ— 10⁹⁴(95-digit number)
93959562188167681770…13161430793921982719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.879 Γ— 10⁹⁡(96-digit number)
18791912437633536354…26322861587843965439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,637,212 XPMΒ·at block #6,799,146 Β· updates every 60s
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