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Block #74,628

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 12:08:03 PM Β· Difficulty 8.9956 Β· 6,723,512 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
38bd5d8cd955a163454cd5363c45cabd21f745a460a196b58c372999181952c7
View on Chainz β†—

Height

#74,628

Difficulty

8.995626

Transactions

1

Size

202 B

Version

2

Bits

08fee15b

Nonce

23

Timestamp

7/21/2013, 12:08:03 PM

Confirmations

6,723,512

Merkle Root

d55fb39a2d1a85c088422aa5f2f0378550a0ed5c8a995241e5d6b61b3622c943
Transactions (1)
Coinbased55fb39a2d1a85…d6b61b3622c943
1 in β†’ 1 out12.3400 XPM110 B
APY1J1ZY…FaUv3anE
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.

2.780 Γ— 10⁹⁸(99-digit number)
27803618288800477098…20128158936376176630
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
2.780 Γ— 10⁹⁸(99-digit number)
27803618288800477098…20128158936376176631
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.560 Γ— 10⁹⁸(99-digit number)
55607236577600954197…40256317872752353261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.112 Γ— 10⁹⁹(100-digit number)
11121447315520190839…80512635745504706521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.224 Γ— 10⁹⁹(100-digit number)
22242894631040381679…61025271491009413041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.448 Γ— 10⁹⁹(100-digit number)
44485789262080763358…22050542982018826081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.897 Γ— 10⁹⁹(100-digit number)
88971578524161526716…44101085964037652161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.779 Γ— 10¹⁰⁰(101-digit number)
17794315704832305343…88202171928075304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.558 Γ— 10¹⁰⁰(101-digit number)
35588631409664610686…76404343856150608641
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 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 8
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 74628

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 38bd5d8cd955a163454cd5363c45cabd21f745a460a196b58c372999181952c7

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 #74,628 on Chainz β†—
Circulating Supply:57,629,117 XPMΒ·at block #6,798,139 Β· updates every 60s
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