Home/Chain Registry/Block #61,783

Block #61,783

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:20:51 PM · Difficulty 8.9743 · 6,735,633 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9055e614d131cdef6e7b929e761866eb61415949d16d650dec67213bb43d410

View on Chainz ↗

Height

#61,783

Difficulty

8.974300

Transactions

Size

429 B

Version

Bits

08f96bbe

Nonce

231

Timestamp

7/18/2013, 3:20:51 PM

Confirmations

6,735,633

Merkle Root

b2320d13333e0b029b37abb0b7f2c4c7ebed9a0e3d0d648e022557e5168817b3

Transactions (2)

Coinbase449676cabb1948…aaf644e50c7541

1 in → 1 out12.4100 XPM110 B

Aedtg5Z7…gGiT69aT

dc2ce007d7bb99…37801ac602d860

1 in → 2 out9.9900 XPM226 B

ALVbrX3z…zXTJ78wp AYw1Zhc6…TxbjH12x

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.

9.226 × 10¹⁰¹(102-digit number)

92269729983876931055…78611199916966371550

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

9.226 × 10¹⁰¹(102-digit number)

92269729983876931055…78611199916966371549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.226 × 10¹⁰¹(102-digit number)

92269729983876931055…78611199916966371551

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

1.845 × 10¹⁰²(103-digit number)

18453945996775386211…57222399833932743099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.845 × 10¹⁰²(103-digit number)

18453945996775386211…57222399833932743101

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

3.690 × 10¹⁰²(103-digit number)

36907891993550772422…14444799667865486199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.690 × 10¹⁰²(103-digit number)

36907891993550772422…14444799667865486201

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

7.381 × 10¹⁰²(103-digit number)

73815783987101544844…28889599335730972399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.381 × 10¹⁰²(103-digit number)

73815783987101544844…28889599335730972401

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

1.476 × 10¹⁰³(104-digit number)

14763156797420308968…57779198671461944799

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 61783

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 a9055e614d131cdef6e7b929e761866eb61415949d16d650dec67213bb43d410

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 #61,783 on Chainz ↗