XPM Prime Explorer symbol
XPMPrime Explorer

Block #70,016

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 11:31:53 AM Β· Difficulty 8.9917 Β· 6,726,047 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9631e4eccf09b903be5c86e71cfd26bf2a46425c51d71907c77250e3f873ea81
View on Chainz β†—

Height

#70,016

Difficulty

8.991661

Transactions

1

Size

198 B

Version

2

Bits

08fddd77

Nonce

59

Timestamp

7/20/2013, 11:31:53 AM

Confirmations

6,726,047

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

74babe5892f1d043619ba37251b8741724ce5909404f260c2cb7ed4430432a6b
Transactions (1)
Coinbase74babe5892f1d0…b7ed4430432a6b
1 in β†’ 1 out12.3500 XPM110 B
AXSFye4r…ADf1YWCU
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.

1.252 Γ— 10⁹¹(92-digit number)
12529086066159920531…46888213754425655659
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
1.252 Γ— 10⁹¹(92-digit number)
12529086066159920531…46888213754425655659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.505 Γ— 10⁹¹(92-digit number)
25058172132319841063…93776427508851311319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.011 Γ— 10⁹¹(92-digit number)
50116344264639682126…87552855017702622639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.002 Γ— 10⁹²(93-digit number)
10023268852927936425…75105710035405245279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.004 Γ— 10⁹²(93-digit number)
20046537705855872850…50211420070810490559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.009 Γ— 10⁹²(93-digit number)
40093075411711745700…00422840141620981119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.018 Γ— 10⁹²(93-digit number)
80186150823423491401…00845680283241962239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.603 Γ— 10⁹³(94-digit number)
16037230164684698280…01691360566483924479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.207 Γ— 10⁹³(94-digit number)
32074460329369396560…03382721132967848959
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:57,612,598 XPMΒ·at block #6,796,062 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK