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Home/Chain Registry/Block #1,357,946

Block #1,357,946

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/6/2015, 6:05:46 PM Β· Difficulty 10.8295 Β· 5,468,944 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
980e9da5380a76c71196b3150fd85b86f28ea536fb923dd385bc1b738c39c86a
View on Chainz β†—

Difficulty

10.829549

Transactions

1

Size

243 B

Version

2

Bits

0ad45d4e

Nonce

619,585,310

Timestamp

12/6/2015, 6:05:46 PM

Confirmations

5,468,944

Merkle Root

edb8af838673237d4c5d24c40b08a103d0b868576e6f5c5f35a8548c7e2a8fcb
Transactions (1)
Coinbaseedb8af83867323…a8548c7e2a8fcb
1 in β†’ 2 out8.5100 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…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.

3.051 Γ— 10⁹⁷(98-digit number)
30518616719111378159…92545876897411189760
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
3.051 Γ— 10⁹⁷(98-digit number)
30518616719111378159…92545876897411189759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.103 Γ— 10⁹⁷(98-digit number)
61037233438222756318…85091753794822379519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁸(99-digit number)
12207446687644551263…70183507589644759039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.441 Γ— 10⁹⁸(99-digit number)
24414893375289102527…40367015179289518079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.882 Γ— 10⁹⁸(99-digit number)
48829786750578205054…80734030358579036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.765 Γ— 10⁹⁸(99-digit number)
97659573501156410109…61468060717158072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.953 Γ— 10⁹⁹(100-digit number)
19531914700231282021…22936121434316144639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.906 Γ— 10⁹⁹(100-digit number)
39063829400462564043…45872242868632289279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.812 Γ— 10⁹⁹(100-digit number)
78127658800925128087…91744485737264578559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.562 Γ— 10¹⁰⁰(101-digit number)
15625531760185025617…83488971474529157119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.125 Γ— 10¹⁰⁰(101-digit number)
31251063520370051235…66977942949058314239
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 1357946

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 980e9da5380a76c71196b3150fd85b86f28ea536fb923dd385bc1b738c39c86a

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 #1,357,946 on Chainz β†—
Circulating Supply:57,859,285 XPMΒ·at block #6,826,889 Β· updates every 60s
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