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Block #58,845

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2013, 10:56:11 PM Β· Difficulty 8.9620 Β· 6,736,974 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c0b1d0e45356704863c91e3a4e23bc4fd581d862231fb57b2375fefc6684f8ef
View on Chainz β†—

Height

#58,845

Difficulty

8.962018

Transactions

2

Size

538 B

Version

2

Bits

08f646ca

Nonce

768

Timestamp

7/17/2013, 10:56:11 PM

Confirmations

6,736,974

Mined by

⛏️ P2SHAc9FAiLXKgp9ekDGqqZmCo85Z8y5M5E5hz

Merkle Root

5c7a5a8270f1779b983b9b612ecbbf5d0e019feceab916a0f86c7302ac66c81a
Transactions (2)
Coinbasee6fbfeb4d33c68…fd90e91d0bb2d8
1 in β†’ 1 out12.4480 XPM110 B
Ac9FAiLX…y5M5E5hz
773807cae3d2f9…5559a8ac0c3295
2 in β†’ 1 out4.0000 XPM341 B
AaH4r4k9…NiR1RUYB
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.

3.863 Γ— 10⁸⁸(89-digit number)
38632494592035794748…22229617305158828699
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
3.863 Γ— 10⁸⁸(89-digit number)
38632494592035794748…22229617305158828699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.726 Γ— 10⁸⁸(89-digit number)
77264989184071589496…44459234610317657399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.545 Γ— 10⁸⁹(90-digit number)
15452997836814317899…88918469220635314799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.090 Γ— 10⁸⁹(90-digit number)
30905995673628635798…77836938441270629599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.181 Γ— 10⁸⁹(90-digit number)
61811991347257271597…55673876882541259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.236 Γ— 10⁹⁰(91-digit number)
12362398269451454319…11347753765082518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.472 Γ— 10⁹⁰(91-digit number)
24724796538902908638…22695507530165036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.944 Γ— 10⁹⁰(91-digit number)
49449593077805817277…45391015060330073599
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:57,610,634 XPMΒ·at block #6,795,818 Β· updates every 60s
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