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Home/Chain Registry/Block #2,133,625

Block #2,133,625

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 3:56:40 PM Β· Difficulty 10.9093 Β· 4,707,122 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fb7451185b571f6b851ee6763d57b771fecd2d15d4f2fa6ea67c78e6ce1bd473
View on Chainz β†—

Difficulty

10.909349

Transactions

2

Size

687 B

Version

2

Bits

0ae8cb14

Nonce

1,040,229,437

Timestamp

5/26/2017, 3:56:40 PM

Confirmations

4,707,122

Merkle Root

1503ff85119e10c010936fec47c383f144648ff498ba67f479e72f2fcf0edc1d
Transactions (2)
Coinbase7e9cdc9380468c…8630628d1346d5
1 in β†’ 1 out8.4000 XPM109 B
AY9BpANs…MLahDfc6
462b3e9a234b4c…f681956b024bf6
3 in β†’ 1 out1.8493 XPM489 B
AerbaHnR…RPRuTbo3
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.

1.417 Γ— 10⁹³(94-digit number)
14178248754231882058…58278189066181149440
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
1.417 Γ— 10⁹³(94-digit number)
14178248754231882058…58278189066181149441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.835 Γ— 10⁹³(94-digit number)
28356497508463764116…16556378132362298881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.671 Γ— 10⁹³(94-digit number)
56712995016927528232…33112756264724597761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.134 Γ— 10⁹⁴(95-digit number)
11342599003385505646…66225512529449195521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.268 Γ— 10⁹⁴(95-digit number)
22685198006771011292…32451025058898391041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.537 Γ— 10⁹⁴(95-digit number)
45370396013542022585…64902050117796782081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.074 Γ— 10⁹⁴(95-digit number)
90740792027084045171…29804100235593564161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.814 Γ— 10⁹⁡(96-digit number)
18148158405416809034…59608200471187128321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.629 Γ— 10⁹⁡(96-digit number)
36296316810833618068…19216400942374256641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.259 Γ— 10⁹⁡(96-digit number)
72592633621667236137…38432801884748513281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.451 Γ— 10⁹⁢(97-digit number)
14518526724333447227…76865603769497026561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2133625

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 fb7451185b571f6b851ee6763d57b771fecd2d15d4f2fa6ea67c78e6ce1bd473

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 #2,133,625 on Chainz β†—
Circulating Supply:57,970,318 XPMΒ·at block #6,840,746 Β· updates every 60s
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