XPM Prime Explorer symbol
XPMPrime Explorer

Block #86,713

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2013, 8:22:38 AM Β· Difficulty 9.2864 Β· 6,715,877 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bed28aed5f3b4dbb1dfa837d2cca38d0256d53aa7301bfb321649efc9d34fabe
View on Chainz β†—

Height

#86,713

Difficulty

9.286381

Transactions

3

Size

1.08 KB

Version

2

Bits

0949503f

Nonce

157

Timestamp

7/28/2013, 8:22:38 AM

Confirmations

6,715,877

Mined by

⛏️ P2SHAZMfqce8XGS4vCH8qsMnDXwrFEWvZvfvUR

Merkle Root

a64aff59df93ecb6cae2000745cd6dcb0fc910e1ee29f7f8f057b330b3bfa783
Transactions (3)
Coinbaseee3ed553d904b2…a7baed162af713
1 in β†’ 1 out11.6000 XPM110 B
AZMfqce8…WvZvfvUR
5e981d8a76355a…483fb545b78f65
4 in β†’ 1 out124.9900 XPM636 B
AJV9J7t5…G9F5PrK8
b9dd311042b8f2…7d385ffe3c0796
2 in β†’ 1 out23.2100 XPM272 B
ARP8QpQi…sFuEcay7
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.

3.009 Γ— 10⁹³(94-digit number)
30094212927214918551…76607445411397364879
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
3.009 Γ— 10⁹³(94-digit number)
30094212927214918551…76607445411397364879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.018 Γ— 10⁹³(94-digit number)
60188425854429837102…53214890822794729759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁴(95-digit number)
12037685170885967420…06429781645589459519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.407 Γ— 10⁹⁴(95-digit number)
24075370341771934841…12859563291178919039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.815 Γ— 10⁹⁴(95-digit number)
48150740683543869682…25719126582357838079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.630 Γ— 10⁹⁴(95-digit number)
96301481367087739364…51438253164715676159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.926 Γ— 10⁹⁡(96-digit number)
19260296273417547872…02876506329431352319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.852 Γ— 10⁹⁡(96-digit number)
38520592546835095745…05753012658862704639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.704 Γ— 10⁹⁡(96-digit number)
77041185093670191491…11506025317725409279
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:57,664,738 XPMΒ·at block #6,802,589 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