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Block #61,624

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 2:27:09 PM Β· Difficulty 8.9738 Β· 6,744,042 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
81dfbc323aef8c1280f5751d945442a28361cb02909e2a5c0480d2035ced42ea
View on Chainz β†—

Height

#61,624

Difficulty

8.973779

Transactions

1

Size

197 B

Version

2

Bits

08f94993

Nonce

162

Timestamp

7/18/2013, 2:27:09 PM

Confirmations

6,744,042

Mined by

⛏️ P2SHAXY6feytV6ZxBQJFLAbLwdMRw9oghmWWGf

Merkle Root

5a304ba22b7ec88af0cd7a9029c210875785de446f0e3902c1b7f66eec341070
Transactions (1)
Coinbase5a304ba22b7ec8…b7f66eec341070
1 in β†’ 1 out12.4000 XPM109 B
AXY6feyt…oghmWWGf
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.

1.837 Γ— 10⁹⁰(91-digit number)
18370852326250309997…28880959638075440609
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
1.837 Γ— 10⁹⁰(91-digit number)
18370852326250309997…28880959638075440609
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.674 Γ— 10⁹⁰(91-digit number)
36741704652500619995…57761919276150881219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.348 Γ— 10⁹⁰(91-digit number)
73483409305001239990…15523838552301762439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.469 Γ— 10⁹¹(92-digit number)
14696681861000247998…31047677104603524879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.939 Γ— 10⁹¹(92-digit number)
29393363722000495996…62095354209207049759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.878 Γ— 10⁹¹(92-digit number)
58786727444000991992…24190708418414099519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.175 Γ— 10⁹²(93-digit number)
11757345488800198398…48381416836828199039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.351 Γ— 10⁹²(93-digit number)
23514690977600396796…96762833673656398079
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:57,689,406 XPMΒ·at block #6,805,665 Β· updates every 60s
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