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Home/Chain Registry/Block #2,139,105

Block #2,139,105

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/31/2017, 11:12:54 AM Β· Difficulty 10.8797 Β· 4,705,803 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1ba132f9be5acc2d0157dd6b82dc8fc4843fec6274b0c6db2c7e8a70d62c44be
View on Chainz β†—

Difficulty

10.879667

Transactions

1

Size

200 B

Version

2

Bits

0ae131d6

Nonce

1,990,377,073

Timestamp

5/31/2017, 11:12:54 AM

Confirmations

4,705,803

Merkle Root

587df81decc54a8888e43922e62f4631f9845d1ccb6858f9b19cfabc96c1d628
Transactions (1)
Coinbase587df81decc54a…9cfabc96c1d628
1 in β†’ 1 out8.4300 XPM109 B
AWS9Upzd…cUXYDDY4
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.

6.280 Γ— 10⁹⁢(97-digit number)
62804770366919085946…17435687859785845760
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
6.280 Γ— 10⁹⁢(97-digit number)
62804770366919085946…17435687859785845761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.256 Γ— 10⁹⁷(98-digit number)
12560954073383817189…34871375719571691521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.512 Γ— 10⁹⁷(98-digit number)
25121908146767634378…69742751439143383041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.024 Γ— 10⁹⁷(98-digit number)
50243816293535268757…39485502878286766081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.004 Γ— 10⁹⁸(99-digit number)
10048763258707053751…78971005756573532161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.009 Γ— 10⁹⁸(99-digit number)
20097526517414107502…57942011513147064321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.019 Γ— 10⁹⁸(99-digit number)
40195053034828215005…15884023026294128641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.039 Γ— 10⁹⁸(99-digit number)
80390106069656430011…31768046052588257281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.607 Γ— 10⁹⁹(100-digit number)
16078021213931286002…63536092105176514561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.215 Γ— 10⁹⁹(100-digit number)
32156042427862572004…27072184210353029121
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 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
UncommonChain length 10
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 2139105

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 1ba132f9be5acc2d0157dd6b82dc8fc4843fec6274b0c6db2c7e8a70d62c44be

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 #2,139,105 on Chainz β†—
Circulating Supply:58,003,679 XPMΒ·at block #6,844,907 Β· updates every 60s
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