XPM Prime Explorer symbol
XPMPrime Explorer

Block #72,471

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 12:23:35 AM Β· Difficulty 8.9941 Β· 6,732,495 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
355d6a9b5fb4eb2a41d954ec0d48baa9232130355cf5e4711c493c795c6817d9
View on Chainz β†—

Height

#72,471

Difficulty

8.994091

Transactions

1

Size

197 B

Version

2

Bits

08fe7cc7

Nonce

520

Timestamp

7/21/2013, 12:23:35 AM

Confirmations

6,732,495

Mined by

⛏️ P2SHAPxUMipnp1rZxF8iz1xZQD73Wi2zpbPwcA

Merkle Root

fb0164ff66f02f376539ddec4828699371e999ee6a19bd1155271308da9812c4
Transactions (1)
Coinbasefb0164ff66f02f…271308da9812c4
1 in β†’ 1 out12.3400 XPM110 B
APxUMipn…2zpbPwcA
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.

2.085 Γ— 10⁸⁷(88-digit number)
20851449932699645220…66861393869337992959
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
2.085 Γ— 10⁸⁷(88-digit number)
20851449932699645220…66861393869337992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.170 Γ— 10⁸⁷(88-digit number)
41702899865399290441…33722787738675985919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.340 Γ— 10⁸⁷(88-digit number)
83405799730798580883…67445575477351971839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.668 Γ— 10⁸⁸(89-digit number)
16681159946159716176…34891150954703943679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.336 Γ— 10⁸⁸(89-digit number)
33362319892319432353…69782301909407887359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.672 Γ— 10⁸⁸(89-digit number)
66724639784638864706…39564603818815774719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.334 Γ— 10⁸⁹(90-digit number)
13344927956927772941…79129207637631549439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.668 Γ— 10⁸⁹(90-digit number)
26689855913855545882…58258415275263098879
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:57,683,795 XPMΒ·at block #6,804,965 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