XPM Prime Explorer symbol
XPMPrime Explorer

Block #149,013

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 2:21:09 AM Β· Difficulty 9.8567 Β· 6,653,618 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b59a64a2dcb6521615adcd7341a4d3fd2d2795e528f980f7e5d2e78f36397092
View on Chainz β†—

Height

#149,013

Difficulty

9.856679

Transactions

1

Size

199 B

Version

2

Bits

09db4f55

Nonce

62,797

Timestamp

9/4/2013, 2:21:09 AM

Confirmations

6,653,618

Mined by

⛏️ P2SHARBvr1evuYzdjmXQBMTxCmA4hCNg7YPkPH

Merkle Root

6d191b6f1d36d5b0e3f9cb9dda4cf41f09742bcc8d92fcce90e209c3223620f3
Transactions (1)
Coinbase6d191b6f1d36d5…e209c3223620f3
1 in β†’ 1 out10.2800 XPM109 B
ARBvr1ev…Ng7YPkPH
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.

1.142 Γ— 10⁹⁴(95-digit number)
11420161360138496673…64664501092292001439
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
1.142 Γ— 10⁹⁴(95-digit number)
11420161360138496673…64664501092292001439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁴(95-digit number)
22840322720276993347…29329002184584002879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.568 Γ— 10⁹⁴(95-digit number)
45680645440553986694…58658004369168005759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.136 Γ— 10⁹⁴(95-digit number)
91361290881107973388…17316008738336011519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.827 Γ— 10⁹⁡(96-digit number)
18272258176221594677…34632017476672023039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.654 Γ— 10⁹⁡(96-digit number)
36544516352443189355…69264034953344046079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.308 Γ— 10⁹⁡(96-digit number)
73089032704886378710…38528069906688092159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.461 Γ— 10⁹⁢(97-digit number)
14617806540977275742…77056139813376184319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.923 Γ— 10⁹⁢(97-digit number)
29235613081954551484…54112279626752368639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.847 Γ— 10⁹⁢(97-digit number)
58471226163909102968…08224559253504737279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,665,063 XPMΒ·at block #6,802,630 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