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Home/Chain Registry/Block #1,527,307

Block #1,527,307

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2016, 9:01:13 AM Β· Difficulty 10.6079 Β· 5,288,702 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8b2df89fa2c7b653276a4b5d6dcea53f85a09ea79da756348ad0f35bb3d0a762
View on Chainz β†—

Difficulty

10.607945

Transactions

2

Size

538 B

Version

2

Bits

0a9ba244

Nonce

2,052,603,096

Timestamp

4/5/2016, 9:01:13 AM

Confirmations

5,288,702

Merkle Root

4a1e444a0196fe3c7fc1892b95ca2703195f3a62c3588d41fc9f68eb561e944c
Transactions (2)
Coinbase5339b6d35a5d58…6c734d141b831f
1 in β†’ 1 out8.8800 XPM109 B
AJoiH4mC…Fmxpua1z
c548ac2d4b0a38…01821a879c42c8
2 in β†’ 1 out5.1000 XPM340 B
AW9z6iyE…ZMok5rfx
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.

3.869 Γ— 10⁹²(93-digit number)
38695420297326992632…79634919035008928640
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
3.869 Γ— 10⁹²(93-digit number)
38695420297326992632…79634919035008928639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.739 Γ— 10⁹²(93-digit number)
77390840594653985265…59269838070017857279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.547 Γ— 10⁹³(94-digit number)
15478168118930797053…18539676140035714559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.095 Γ— 10⁹³(94-digit number)
30956336237861594106…37079352280071429119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.191 Γ— 10⁹³(94-digit number)
61912672475723188212…74158704560142858239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.238 Γ— 10⁹⁴(95-digit number)
12382534495144637642…48317409120285716479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.476 Γ— 10⁹⁴(95-digit number)
24765068990289275284…96634818240571432959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.953 Γ— 10⁹⁴(95-digit number)
49530137980578550569…93269636481142865919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.906 Γ— 10⁹⁴(95-digit number)
99060275961157101139…86539272962285731839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.981 Γ— 10⁹⁡(96-digit number)
19812055192231420227…73078545924571463679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.962 Γ— 10⁹⁡(96-digit number)
39624110384462840455…46157091849142927359
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 1527307

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 8b2df89fa2c7b653276a4b5d6dcea53f85a09ea79da756348ad0f35bb3d0a762

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 #1,527,307 on Chainz β†—
Circulating Supply:57,772,189 XPMΒ·at block #6,816,008 Β· updates every 60s
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