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Block #127,152

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2013, 8:22:32 AM Β· Difficulty 9.7832 Β· 6,685,220 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e3b7d5a6300091b60d93bc307369e3c2ca4c7d253b4ff8d31dbb739fb8a3176a
View on Chainz β†—

Height

#127,152

Difficulty

9.783202

Transactions

1

Size

201 B

Version

2

Bits

09c87ff3

Nonce

245,025

Timestamp

8/21/2013, 8:22:32 AM

Confirmations

6,685,220

Merkle Root

f3f2208b0002147f937c093e9d59cfc4679c96d8a13a04bc459f3a38d282604e
Transactions (1)
Coinbasef3f2208b000214…9f3a38d282604e
1 in β†’ 1 out10.4300 XPM109 B
AcMYZ4y2…SA8KujQk
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.

1.714 Γ— 10⁹⁸(99-digit number)
17140277531902411187…75893564861359765060
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
1.714 Γ— 10⁹⁸(99-digit number)
17140277531902411187…75893564861359765059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.428 Γ— 10⁹⁸(99-digit number)
34280555063804822375…51787129722719530119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.856 Γ— 10⁹⁸(99-digit number)
68561110127609644751…03574259445439060239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁹(100-digit number)
13712222025521928950…07148518890878120479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁹(100-digit number)
27424444051043857900…14297037781756240959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.484 Γ— 10⁹⁹(100-digit number)
54848888102087715801…28594075563512481919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.096 Γ— 10¹⁰⁰(101-digit number)
10969777620417543160…57188151127024963839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.193 Γ— 10¹⁰⁰(101-digit number)
21939555240835086320…14376302254049927679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.387 Γ— 10¹⁰⁰(101-digit number)
43879110481670172641…28752604508099855359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 127152

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 e3b7d5a6300091b60d93bc307369e3c2ca4c7d253b4ff8d31dbb739fb8a3176a

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 #127,152 on Chainz β†—
Circulating Supply:57,742,997 XPMΒ·at block #6,812,371 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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