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Block #137,688

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2013, 11:18:39 PM Β· Difficulty 9.8225 Β· 6,678,482 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0e10fa54c9ca37ca94851705536517fe2a80d1364f38b143e2c1fff8213ceccf
View on Chainz β†—

Height

#137,688

Difficulty

9.822505

Transactions

1

Size

198 B

Version

2

Bits

09d28fb4

Nonce

163,003

Timestamp

8/27/2013, 11:18:39 PM

Confirmations

6,678,482

Merkle Root

bb8e268ed37425c4082e30b38a9acaed7509b76b3ebda24615b9eee9c4117830
Transactions (1)
Coinbasebb8e268ed37425…b9eee9c4117830
1 in β†’ 1 out10.3500 XPM109 B
APhf7UNh…GDFABLcg
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.

1.242 Γ— 10⁹²(93-digit number)
12428394335708620259…78881240433782760600
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
1.242 Γ— 10⁹²(93-digit number)
12428394335708620259…78881240433782760601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.485 Γ— 10⁹²(93-digit number)
24856788671417240518…57762480867565521201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.971 Γ— 10⁹²(93-digit number)
49713577342834481036…15524961735131042401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.942 Γ— 10⁹²(93-digit number)
99427154685668962072…31049923470262084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.988 Γ— 10⁹³(94-digit number)
19885430937133792414…62099846940524169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.977 Γ— 10⁹³(94-digit number)
39770861874267584829…24199693881048339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.954 Γ— 10⁹³(94-digit number)
79541723748535169658…48399387762096678401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.590 Γ— 10⁹⁴(95-digit number)
15908344749707033931…96798775524193356801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.181 Γ— 10⁹⁴(95-digit number)
31816689499414067863…93597551048386713601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.363 Γ— 10⁹⁴(95-digit number)
63633378998828135726…87195102096773427201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 137688

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 0e10fa54c9ca37ca94851705536517fe2a80d1364f38b143e2c1fff8213ceccf

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 #137,688 on Chainz β†—
Circulating Supply:57,773,483 XPMΒ·at block #6,816,169 Β· updates every 60s
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