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.

1.339 × 10⁹⁴(95-digit number)

13397297447520582492…64169667918882324480

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

1.339 × 10⁹⁴(95-digit number)

13397297447520582492…64169667918882324481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.679 × 10⁹⁴(95-digit number)

26794594895041164985…28339335837764648961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.358 × 10⁹⁴(95-digit number)

53589189790082329971…56678671675529297921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.071 × 10⁹⁵(96-digit number)

10717837958016465994…13357343351058595841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.143 × 10⁹⁵(96-digit number)

21435675916032931988…26714686702117191681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.287 × 10⁹⁵(96-digit number)

42871351832065863976…53429373404234383361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.574 × 10⁹⁵(96-digit number)

85742703664131727953…06858746808468766721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.714 × 10⁹⁶(97-digit number)

17148540732826345590…13717493616937533441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.429 × 10⁹⁶(97-digit number)

34297081465652691181…27434987233875066881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.859 × 10⁹⁶(97-digit number)

68594162931305382362…54869974467750133761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.371 × 10⁹⁷(98-digit number)

13718832586261076472…09739948935500267521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

2.743 × 10⁹⁷(98-digit number)

27437665172522152945…19479897871000535041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^12 × origin + 1

5.487 × 10⁹⁷(98-digit number)

54875330345044305890…38959795742001070081

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 13 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

LegendaryChain length 13

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 2654715

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 2f87f2e8946dd21dfdaab4224d5f3f470be29f437bc2c2cf07cae8733590dd15

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 #2,654,715 on Chainz ↗

Block #2,654,715

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