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Block #277,060

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/27/2013, 10:37:22 AM Β· Difficulty 9.9650 Β· 6,536,870 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f499ebb460ff48b51459850aad0deb5bd4c8f5d009ffeb5a47176cdd9a98145d
View on Chainz β†—

Height

#277,060

Difficulty

9.965038

Transactions

1

Size

200 B

Version

2

Bits

09f70cb3

Nonce

71,594

Timestamp

11/27/2013, 10:37:22 AM

Confirmations

6,536,870

Merkle Root

218e9f23bcf7ec00ce333b4a5460460b01965b36c25948e0c7a15b8087cbee54
Transactions (1)
Coinbase218e9f23bcf7ec…a15b8087cbee54
1 in β†’ 1 out10.0600 XPM109 B
ASvp9L2G…DTKVZ2Wy
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.

2.207 Γ— 10⁹⁷(98-digit number)
22079688664279355174…09703330103090672960
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
2.207 Γ— 10⁹⁷(98-digit number)
22079688664279355174…09703330103090672959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.415 Γ— 10⁹⁷(98-digit number)
44159377328558710348…19406660206181345919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.831 Γ— 10⁹⁷(98-digit number)
88318754657117420697…38813320412362691839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.766 Γ— 10⁹⁸(99-digit number)
17663750931423484139…77626640824725383679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.532 Γ— 10⁹⁸(99-digit number)
35327501862846968278…55253281649450767359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.065 Γ— 10⁹⁸(99-digit number)
70655003725693936557…10506563298901534719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.413 Γ— 10⁹⁹(100-digit number)
14131000745138787311…21013126597803069439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.826 Γ— 10⁹⁹(100-digit number)
28262001490277574623…42026253195606138879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.652 Γ— 10⁹⁹(100-digit number)
56524002980555149246…84052506391212277759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.130 Γ— 10¹⁰⁰(101-digit number)
11304800596111029849…68105012782424555519
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 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
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 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 277060

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 f499ebb460ff48b51459850aad0deb5bd4c8f5d009ffeb5a47176cdd9a98145d

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 #277,060 on Chainz β†—
Circulating Supply:57,755,515 XPMΒ·at block #6,813,929 Β· updates every 60s
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