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Home/Chain Registry/Block #2,139,609

Block #2,139,609

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2017, 8:27:34 PM Β· Difficulty 10.8785 Β· 4,699,410 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b2fd4ed586150c8f5373590c2fe1159c04b20e0b3769102887fc6d8c8ad3328c
View on Chainz β†—

Difficulty

10.878475

Transactions

2

Size

2.44 KB

Version

2

Bits

0ae0e3c2

Nonce

1,602,868,538

Timestamp

5/31/2017, 8:27:34 PM

Confirmations

4,699,410

Merkle Root

2b4c9e562c87dd6f1c83aaf26e3b9f45130a0022a2fb5effa7cb7d2c93c8dc85
Transactions (2)
Coinbase0f9ce2248f6c97…ca2754710763ff
1 in β†’ 1 out8.4700 XPM109 B
AWxNZ4UK…C9ujRMt1
fc5872fd0a2f36…11f08afc5cbf42
15 in β†’ 2 out42.4060 XPM2.25 KB
AYAuRWxY…Rg3t4M63AGCFjQA5…TYFqPSMb
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.

1.586 Γ— 10⁹⁡(96-digit number)
15868557864061746583…14261080584350177280
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
1.586 Γ— 10⁹⁡(96-digit number)
15868557864061746583…14261080584350177279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.173 Γ— 10⁹⁡(96-digit number)
31737115728123493166…28522161168700354559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.347 Γ— 10⁹⁡(96-digit number)
63474231456246986332…57044322337400709119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.269 Γ— 10⁹⁢(97-digit number)
12694846291249397266…14088644674801418239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.538 Γ— 10⁹⁢(97-digit number)
25389692582498794532…28177289349602836479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.077 Γ— 10⁹⁢(97-digit number)
50779385164997589065…56354578699205672959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁷(98-digit number)
10155877032999517813…12709157398411345919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.031 Γ— 10⁹⁷(98-digit number)
20311754065999035626…25418314796822691839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.062 Γ— 10⁹⁷(98-digit number)
40623508131998071252…50836629593645383679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.124 Γ— 10⁹⁷(98-digit number)
81247016263996142505…01673259187290767359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.624 Γ— 10⁹⁸(99-digit number)
16249403252799228501…03346518374581534719
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 2139609

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 b2fd4ed586150c8f5373590c2fe1159c04b20e0b3769102887fc6d8c8ad3328c

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 #2,139,609 on Chainz β†—
Circulating Supply:57,956,420 XPMΒ·at block #6,839,018 Β· updates every 60s
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