XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #74,777

Block #74,777

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 12:54:06 PM Β· Difficulty 8.9957 Β· 6,731,194 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2d688cfb31e1b079089bbe3ce9692b7d58fc47727e7b4741ea84dbc53df89ba
View on Chainz β†—

Height

#74,777

Difficulty

8.995719

Transactions

1

Size

201 B

Version

2

Bits

08fee773

Nonce

137

Timestamp

7/21/2013, 12:54:06 PM

Confirmations

6,731,194

Merkle Root

c53f8151aeacad9460eec780ca520398d240832c11d768dc2624e0e4c4569899
Transactions (1)
Coinbasec53f8151aeacad…24e0e4c4569899
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.

2.196 Γ— 10⁹⁢(97-digit number)
21964025709536436660…87383802446541568440
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
2.196 Γ— 10⁹⁢(97-digit number)
21964025709536436660…87383802446541568441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.392 Γ— 10⁹⁢(97-digit number)
43928051419072873321…74767604893083136881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.785 Γ— 10⁹⁢(97-digit number)
87856102838145746643…49535209786166273761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.757 Γ— 10⁹⁷(98-digit number)
17571220567629149328…99070419572332547521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.514 Γ— 10⁹⁷(98-digit number)
35142441135258298657…98140839144665095041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.028 Γ— 10⁹⁷(98-digit number)
70284882270516597314…96281678289330190081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.405 Γ— 10⁹⁸(99-digit number)
14056976454103319462…92563356578660380161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.811 Γ— 10⁹⁸(99-digit number)
28113952908206638925…85126713157320760321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.622 Γ— 10⁹⁸(99-digit number)
56227905816413277851…70253426314641520641
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 74777

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 b2d688cfb31e1b079089bbe3ce9692b7d58fc47727e7b4741ea84dbc53df89ba

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 #74,777 on Chainz β†—
Circulating Supply:57,691,843 XPMΒ·at block #6,805,970 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