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Home/Chain Registry/Block #2,261,160

Block #2,261,160

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2017, 5:26:25 AM Β· Difficulty 10.9519 Β· 4,563,654 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d5434024ef6551eb506d1e1e16ba9d5051be41bd5278f7962eb23e903375bb7e
View on Chainz β†—

Difficulty

10.951914

Transactions

1

Size

242 B

Version

2

Bits

0af3b0a6

Nonce

382,413,464

Timestamp

8/21/2017, 5:26:25 AM

Confirmations

4,563,654

Merkle Root

8f87364b03a4f17ef40dc23b86065001f1f4c1ac481aaa4bfb8c3180335949e1
Transactions (1)
Coinbase8f87364b03a4f1…8c3180335949e1
1 in β†’ 2 out8.3200 XPM152 B
ALxvfnPi…Q7UJUBtbAXbk7f7A…Tx7JECPG
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.

8.675 Γ— 10⁹⁴(95-digit number)
86753887760980933815…89463972803754492600
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.675 Γ— 10⁹⁴(95-digit number)
86753887760980933815…89463972803754492599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.735 Γ— 10⁹⁡(96-digit number)
17350777552196186763…78927945607508985199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.470 Γ— 10⁹⁡(96-digit number)
34701555104392373526…57855891215017970399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.940 Γ— 10⁹⁡(96-digit number)
69403110208784747052…15711782430035940799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.388 Γ— 10⁹⁢(97-digit number)
13880622041756949410…31423564860071881599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.776 Γ— 10⁹⁢(97-digit number)
27761244083513898820…62847129720143763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.552 Γ— 10⁹⁢(97-digit number)
55522488167027797641…25694259440287526399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁷(98-digit number)
11104497633405559528…51388518880575052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁷(98-digit number)
22208995266811119056…02777037761150105599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.441 Γ— 10⁹⁷(98-digit number)
44417990533622238113…05554075522300211199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.883 Γ— 10⁹⁷(98-digit number)
88835981067244476226…11108151044600422399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2261160

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 d5434024ef6551eb506d1e1e16ba9d5051be41bd5278f7962eb23e903375bb7e

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 #2,261,160 on Chainz β†—
Circulating Supply:57,842,589 XPMΒ·at block #6,824,813 Β· updates every 60s
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