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Block #60,711

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 9:28:41 AM Β· Difficulty 8.9703 Β· 6,752,024 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
efed5a19492e4cc71c47738b3eef05fa0da0eb8902144ed74291aacc5e4ee721
View on Chainz β†—

Height

#60,711

Difficulty

8.970315

Transactions

1

Size

200 B

Version

2

Bits

08f8668c

Nonce

95

Timestamp

7/18/2013, 9:28:41 AM

Confirmations

6,752,024

Merkle Root

2c1ff1135f2eb8527e982e3705e0e15cb5a83dde18ab05b964cc8c950e47b353
Transactions (1)
Coinbase2c1ff1135f2eb8…cc8c950e47b353
1 in β†’ 1 out12.4100 XPM109 B
AZay2qDM…v81b8pc6
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.

5.075 Γ— 10⁹⁢(97-digit number)
50750472974814781872…99115746562600000700
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
5.075 Γ— 10⁹⁢(97-digit number)
50750472974814781872…99115746562600000699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁷(98-digit number)
10150094594962956374…98231493125200001399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.030 Γ— 10⁹⁷(98-digit number)
20300189189925912748…96462986250400002799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.060 Γ— 10⁹⁷(98-digit number)
40600378379851825497…92925972500800005599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.120 Γ— 10⁹⁷(98-digit number)
81200756759703650995…85851945001600011199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.624 Γ— 10⁹⁸(99-digit number)
16240151351940730199…71703890003200022399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.248 Γ— 10⁹⁸(99-digit number)
32480302703881460398…43407780006400044799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.496 Γ— 10⁹⁸(99-digit number)
64960605407762920796…86815560012800089599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 60711

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 efed5a19492e4cc71c47738b3eef05fa0da0eb8902144ed74291aacc5e4ee721

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 #60,711 on Chainz β†—
Circulating Supply:57,745,921 XPMΒ·at block #6,812,734 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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