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Home/Chain Registry/Block #2,088,595

Block #2,088,595

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/26/2017, 11:08:25 AM Β· Difficulty 10.8752 Β· 4,752,799 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3ee90a2ce5331f430fc308465f29ea06324beb9dcbb15a5f12a65a7e2fc59c35
View on Chainz β†—

Difficulty

10.875207

Transactions

1

Size

199 B

Version

2

Bits

0ae00d91

Nonce

1,492,545,321

Timestamp

4/26/2017, 11:08:25 AM

Confirmations

4,752,799

Merkle Root

15e23a59420751931b187a2042fce127d0ee24b63171793a8894ae8675a27b57
Transactions (1)
Coinbase15e23a59420751…94ae8675a27b57
1 in β†’ 1 out8.4400 XPM109 B
AZbmDg7H…dYe7HspZ
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.

2.901 Γ— 10⁹⁴(95-digit number)
29011931181219123183…82229532447750696960
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
2.901 Γ— 10⁹⁴(95-digit number)
29011931181219123183…82229532447750696961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.802 Γ— 10⁹⁴(95-digit number)
58023862362438246367…64459064895501393921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.160 Γ— 10⁹⁡(96-digit number)
11604772472487649273…28918129791002787841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.320 Γ— 10⁹⁡(96-digit number)
23209544944975298547…57836259582005575681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.641 Γ— 10⁹⁡(96-digit number)
46419089889950597094…15672519164011151361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.283 Γ— 10⁹⁡(96-digit number)
92838179779901194188…31345038328022302721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.856 Γ— 10⁹⁢(97-digit number)
18567635955980238837…62690076656044605441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.713 Γ— 10⁹⁢(97-digit number)
37135271911960477675…25380153312089210881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.427 Γ— 10⁹⁢(97-digit number)
74270543823920955350…50760306624178421761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.485 Γ— 10⁹⁷(98-digit number)
14854108764784191070…01520613248356843521
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 2088595

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 3ee90a2ce5331f430fc308465f29ea06324beb9dcbb15a5f12a65a7e2fc59c35

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 #2,088,595 on Chainz β†—
Circulating Supply:57,975,524 XPMΒ·at block #6,841,393 Β· updates every 60s
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