Home/Chain Registry/Block #2,359,908

Block #2,359,908

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/31/2017, 3:11:45 PM · Difficulty 10.8970 · 4,479,531 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9814180a51a12115c9cba1b24ab2cedcb5d2deab63cbd782ceb46d22e2cb7660

View on Chainz ↗

Height

#2,359,908

Difficulty

10.896985

Transactions

Size

2.19 KB

Version

Bits

0ae5a0d6

Nonce

2,092,527,226

Timestamp

10/31/2017, 3:11:45 PM

Confirmations

4,479,531

Merkle Root

ee3ebbae673cd605fae262f83fad6f29cac69bb4f255dc14a66b63b5bd6fb6de

Transactions (3)

Coinbaseeb2280e9999904…bf1e9a446e9dd1

1 in → 1 out8.4400 XPM110 B

ASD7eaFP…8Hchuwpn

2fc22a3235726c…64d920fbacecde

15 in → 2 out122.1031 XPM1.78 KB

AT9TWjeZ…PAdk7Zi8 AZLPmJvs…pDWmzqwB

4d3615f33a2493…0c14b2af3e34ad

1 in → 2 out3.0960 XPM225 B

AcBqcAvR…oAPsG2ut ANwtSRNc…za9KnLoD

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.447 × 10⁹⁵(96-digit number)

44479753034630272911…49367098086445256000

Discovered Prime Numbers

p_k = 2^k × 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.

origin + 1

4.447 × 10⁹⁵(96-digit number)

44479753034630272911…49367098086445256001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.895 × 10⁹⁵(96-digit number)

88959506069260545822…98734196172890512001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.779 × 10⁹⁶(97-digit number)

17791901213852109164…97468392345781024001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.558 × 10⁹⁶(97-digit number)

35583802427704218329…94936784691562048001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.116 × 10⁹⁶(97-digit number)

71167604855408436658…89873569383124096001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.423 × 10⁹⁷(98-digit number)

14233520971081687331…79747138766248192001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.846 × 10⁹⁷(98-digit number)

28467041942163374663…59494277532496384001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.693 × 10⁹⁷(98-digit number)

56934083884326749326…18988555064992768001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.138 × 10⁹⁸(99-digit number)

11386816776865349865…37977110129985536001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.277 × 10⁹⁸(99-digit number)

22773633553730699730…75954220259971072001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

4.554 × 10⁹⁸(99-digit number)

45547267107461399461…51908440519942144001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — 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 →

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 2359908

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 9814180a51a12115c9cba1b24ab2cedcb5d2deab63cbd782ceb46d22e2cb7660

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 → Debug Window → 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 #2,359,908 on Chainz ↗

Block #2,359,908

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