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Home/Chain Registry/Block #49,108

Block #49,108

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2013, 6:35:55 PM Β· Difficulty 8.8588 Β· 6,746,880 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
afb92051a829829e866802dce2f7b20d37334b9182dfce35e6359bf04e509d70
View on Chainz β†—

Height

#49,108

Difficulty

8.858773

Transactions

2

Size

1.94 KB

Version

2

Bits

08dbd885

Nonce

64

Timestamp

7/15/2013, 6:35:55 PM

Confirmations

6,746,880

Merkle Root

0dced4c9aafda631b94c4a65919c8469bd4bb319cbb865566c9a378fcd2fed46
Transactions (2)
Coinbase25395fd98b9c08…c0ff746a02ef55
1 in β†’ 1 out12.7800 XPM110 B
AQ7FC9gt…ogUwBDMy
031049b071c6b6…2504813399624e
15 in β†’ 2 out249.8500 XPM1.75 KB
AXFxzans…F6s3D6nHATcFpcF1…Bv1WYRrn
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.

9.386 Γ— 10⁸⁷(88-digit number)
93862965569780049857…89436066869266327010
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
9.386 Γ— 10⁸⁷(88-digit number)
93862965569780049857…89436066869266327011
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.877 Γ— 10⁸⁸(89-digit number)
18772593113956009971…78872133738532654021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.754 Γ— 10⁸⁸(89-digit number)
37545186227912019942…57744267477065308041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.509 Γ— 10⁸⁸(89-digit number)
75090372455824039885…15488534954130616081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.501 Γ— 10⁸⁹(90-digit number)
15018074491164807977…30977069908261232161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.003 Γ— 10⁸⁹(90-digit number)
30036148982329615954…61954139816522464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.007 Γ— 10⁸⁹(90-digit number)
60072297964659231908…23908279633044928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.201 Γ— 10⁹⁰(91-digit number)
12014459592931846381…47816559266089857281
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 49108

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 afb92051a829829e866802dce2f7b20d37334b9182dfce35e6359bf04e509d70

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 #49,108 on Chainz β†—
Circulating Supply:57,611,999 XPMΒ·at block #6,795,987 Β· updates every 60s
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