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Home/Chain Registry/Block #2,129,876

Block #2,129,876

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2017, 1:16:02 AM Β· Difficulty 10.9095 Β· 4,713,436 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6052cadd2bc129fb67c0d4a0b7f66daadeadca039f3963277d0c55bdf8e8cbf5
View on Chainz β†—

Difficulty

10.909459

Transactions

1

Size

243 B

Version

2

Bits

0ae8d248

Nonce

147,663,048

Timestamp

5/24/2017, 1:16:02 AM

Confirmations

4,713,436

Merkle Root

be75a15bb2d6b7da03513337fdd7c908bd65646b1aa24ffc2f8947b7af6b66bc
Transactions (1)
Coinbasebe75a15bb2d6b7…8947b7af6b66bc
1 in β†’ 2 out8.3900 XPM152 B
AKYDsG6N…mdbD4KstALPu3s2c…EJXLjVFh
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.

2.533 Γ— 10⁹⁷(98-digit number)
25337555731299119774…25016395849824051200
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
2.533 Γ— 10⁹⁷(98-digit number)
25337555731299119774…25016395849824051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.067 Γ— 10⁹⁷(98-digit number)
50675111462598239548…50032791699648102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.013 Γ— 10⁹⁸(99-digit number)
10135022292519647909…00065583399296204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.027 Γ— 10⁹⁸(99-digit number)
20270044585039295819…00131166798592409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.054 Γ— 10⁹⁸(99-digit number)
40540089170078591638…00262333597184819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.108 Γ— 10⁹⁸(99-digit number)
81080178340157183277…00524667194369638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.621 Γ— 10⁹⁹(100-digit number)
16216035668031436655…01049334388739276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.243 Γ— 10⁹⁹(100-digit number)
32432071336062873310…02098668777478553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.486 Γ— 10⁹⁹(100-digit number)
64864142672125746621…04197337554957107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.297 Γ— 10¹⁰⁰(101-digit number)
12972828534425149324…08394675109914214401
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 2129876

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 6052cadd2bc129fb67c0d4a0b7f66daadeadca039f3963277d0c55bdf8e8cbf5

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 #2,129,876 on Chainz β†—
Circulating Supply:57,990,854 XPMΒ·at block #6,843,311 Β· updates every 60s
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