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Block #150,871

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2013, 8:01:53 AM Β· Difficulty 9.8590 Β· 6,644,039 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2cf4c36c7eb110472c2591f88f3b62e2189e69a9e61afd96beacf21866b180fe
View on Chainz β†—

Height

#150,871

Difficulty

9.858950

Transactions

1

Size

200 B

Version

2

Bits

09dbe427

Nonce

60,393

Timestamp

9/5/2013, 8:01:53 AM

Confirmations

6,644,039

Merkle Root

8762ffd72dfb6a6df0a11b88d80a9b42881b2ed8049bc35f5aba3e09b3ea4449
Transactions (1)
Coinbase8762ffd72dfb6a…ba3e09b3ea4449
1 in β†’ 1 out10.2700 XPM109 B
AM3iC3cp…ozTsmSSX
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.

1.036 Γ— 10⁹⁢(97-digit number)
10366571024922829154…17810132757277593360
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.036 Γ— 10⁹⁢(97-digit number)
10366571024922829154…17810132757277593361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.073 Γ— 10⁹⁢(97-digit number)
20733142049845658308…35620265514555186721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.146 Γ— 10⁹⁢(97-digit number)
41466284099691316617…71240531029110373441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.293 Γ— 10⁹⁢(97-digit number)
82932568199382633234…42481062058220746881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.658 Γ— 10⁹⁷(98-digit number)
16586513639876526646…84962124116441493761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.317 Γ— 10⁹⁷(98-digit number)
33173027279753053293…69924248232882987521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.634 Γ— 10⁹⁷(98-digit number)
66346054559506106587…39848496465765975041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.326 Γ— 10⁹⁸(99-digit number)
13269210911901221317…79696992931531950081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.653 Γ— 10⁹⁸(99-digit number)
26538421823802442635…59393985863063900161
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 Second 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.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 150871

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 2cf4c36c7eb110472c2591f88f3b62e2189e69a9e61afd96beacf21866b180fe

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #150,871 on Chainz β†—
Circulating Supply:57,603,319 XPMΒ·at block #6,794,909 Β· updates every 60s
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