Home/Chain Registry/Block #272,917

Block #272,917

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 1:01:40 PM · Difficulty 9.9536 · 6,553,303 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e887fc23f79e5710869ca3da220302b1703a47ed3395813e9f04cba7b733c1c

View on Chainz ↗

Height

#272,917

Difficulty

9.953615

Transactions

Size

211 B

Version

Bits

09f4201e

Nonce

43,140

Timestamp

11/25/2013, 1:01:40 PM

Confirmations

6,553,303

Merkle Root

6e650a9e94dc6cc533180b2d4c0b7220e25df91a8fed270985db9fed396bdbd7

Transactions (1)

Coinbase6e650a9e94dc6c…db9fed396bdbd7

1 in → 1 out10.0800 XPM118 B

AKJG2u2a…zbHftoor

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.

2.057 × 10¹⁰²(103-digit number)

20575692702458323483…90893194893197312000

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

2.057 × 10¹⁰²(103-digit number)

20575692702458323483…90893194893197311999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.057 × 10¹⁰²(103-digit number)

20575692702458323483…90893194893197312001

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

4.115 × 10¹⁰²(103-digit number)

41151385404916646966…81786389786394623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.115 × 10¹⁰²(103-digit number)

41151385404916646966…81786389786394624001

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

8.230 × 10¹⁰²(103-digit number)

82302770809833293933…63572779572789247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.230 × 10¹⁰²(103-digit number)

82302770809833293933…63572779572789248001

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

1.646 × 10¹⁰³(104-digit number)

16460554161966658786…27145559145578495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.646 × 10¹⁰³(104-digit number)

16460554161966658786…27145559145578496001

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

3.292 × 10¹⁰³(104-digit number)

32921108323933317573…54291118291156991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.292 × 10¹⁰³(104-digit number)

32921108323933317573…54291118291156992001

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 272917

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 9e887fc23f79e5710869ca3da220302b1703a47ed3395813e9f04cba7b733c1c

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 #272,917 on Chainz ↗

Block #272,917

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