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Block #602,515

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/26/2014, 8:39:20 AM · Difficulty 10.9132 · 6,196,412 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

c9414a3e25e4409078a25e0b30bc970c949c8e94a940192a2bde5b25795c08e9

View on Chainz ↗

Height

#602,515

Difficulty

10.913161

Transactions

Size

661 B

Version

Bits

0ae9c4e6

Nonce

357,259,035

Timestamp

6/26/2014, 8:39:20 AM

Confirmations

6,196,412

Merkle Root

fee69bc3079a9f7533fb4042fab6871d48ccec07638824e7afc1b48a2a52fb9b

Transactions (3)

Coinbase03a7e5d0e56e2a…dd540113199e06

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

0782f7f0736305…b651aebbd514c3

1 in → 2 out6.2574 XPM226 B

AY3haNzq…9Y3S5pUQ AW6xKVVP…sFp5odmT

2aa89bfc8789ec…38ae0e1ffbca0e

1 in → 2 out6.6999 XPM227 B

AY5uEK6W…2GvncKvW Ae2e83MX…bzxmuQ39

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.

2.702 × 10⁹⁸(99-digit number)

27028120725891192239…87211138779553282560

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 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.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.702 × 10⁹⁸(99-digit number)

27028120725891192239…87211138779553282559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.702 × 10⁹⁸(99-digit number)

27028120725891192239…87211138779553282561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.405 × 10⁹⁸(99-digit number)

54056241451782384478…74422277559106565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.405 × 10⁹⁸(99-digit number)

54056241451782384478…74422277559106565121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.081 × 10⁹⁹(100-digit number)

10811248290356476895…48844555118213130239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.081 × 10⁹⁹(100-digit number)

10811248290356476895…48844555118213130241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.162 × 10⁹⁹(100-digit number)

21622496580712953791…97689110236426260479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.162 × 10⁹⁹(100-digit number)

21622496580712953791…97689110236426260481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.324 × 10⁹⁹(100-digit number)

43244993161425907582…95378220472852520959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.324 × 10⁹⁹(100-digit number)

43244993161425907582…95378220472852520961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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

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 × 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 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 602515

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 c9414a3e25e4409078a25e0b30bc970c949c8e94a940192a2bde5b25795c08e9

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 #602,515 on Chainz ↗