Home/Chain Registry/Block #72,616

Block #72,616

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 1:15:04 AM · Difficulty 8.9942 · 6,719,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

accf2097eb3506799262d675f5c56391e41bd15bf8c87db1c91c33895448bb46

View on Chainz ↗

Height

#72,616

Difficulty

8.994203

Transactions

Size

203 B

Version

Bits

08fe841e

Nonce

203

Timestamp

7/21/2013, 1:15:04 AM

Confirmations

6,719,977

Merkle Root

d30418061efd55a92719479afc4aea14a63babb987e7f27ece7a377f61c76960

Transactions (1)

Coinbased30418061efd55…7a377f61c76960

1 in → 1 out12.3400 XPM110 B

ANCYL9xh…9WyGnqDE

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.

2.435 × 10¹⁰¹(102-digit number)

24352840663077386587…06008567279796837000

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

2.435 × 10¹⁰¹(102-digit number)

24352840663077386587…06008567279796836999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.435 × 10¹⁰¹(102-digit number)

24352840663077386587…06008567279796837001

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

4.870 × 10¹⁰¹(102-digit number)

48705681326154773175…12017134559593673999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.870 × 10¹⁰¹(102-digit number)

48705681326154773175…12017134559593674001

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

9.741 × 10¹⁰¹(102-digit number)

97411362652309546350…24034269119187347999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.741 × 10¹⁰¹(102-digit number)

97411362652309546350…24034269119187348001

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

1.948 × 10¹⁰²(103-digit number)

19482272530461909270…48068538238374695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.948 × 10¹⁰²(103-digit number)

19482272530461909270…48068538238374696001

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

3.896 × 10¹⁰²(103-digit number)

38964545060923818540…96137076476749391999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 72616

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 accf2097eb3506799262d675f5c56391e41bd15bf8c87db1c91c33895448bb46

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 #72,616 on Chainz ↗