Home/Chain Registry/Block #652,771

Block #652,771

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/29/2014, 2:35:04 AM · Difficulty 10.9546 · 6,164,102 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc7a685362d8d150aa273fda72a3ff0299ef23485adb33ee7a9ca7a16d59e571

View on Chainz ↗

Height

#652,771

Difficulty

10.954608

Transactions

Size

1.30 KB

Version

Bits

0af46135

Nonce

1,285,319,037

Timestamp

7/29/2014, 2:35:04 AM

Confirmations

6,164,102

Merkle Root

be1793b1af0bf1fc8fa46c83e54243925df2a2831210b48746bda570076135bf

Transactions (4)

Coinbasecefb155fc563a5…e63707afcdbc9a

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

878f5499fbdd75…a71a500a72b00c

2 in → 2 out11.4785 XPM375 B

AUj25YYg…qXYgMxRq AJzjuYh3…ndhqFVng

18a63dbde0f2ac…ae156058288d95

3 in → 2 out2.0534 XPM522 B

AFtKUKUa…WyLEn4xB AeKNrjNj…1NEq95Ta

4eaae2e4ca6a53…623af868eb78e8

1 in → 2 out1.2844 XPM227 B

ARnGwLf1…7y3NZg6M ANFt86v4…aActXZCc

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.

9.822 × 10⁹⁵(96-digit number)

98224017527900278724…60828539080992817920

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

9.822 × 10⁹⁵(96-digit number)

98224017527900278724…60828539080992817919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.822 × 10⁹⁵(96-digit number)

98224017527900278724…60828539080992817921

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

1.964 × 10⁹⁶(97-digit number)

19644803505580055744…21657078161985635839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.964 × 10⁹⁶(97-digit number)

19644803505580055744…21657078161985635841

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

3.928 × 10⁹⁶(97-digit number)

39289607011160111489…43314156323971271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.928 × 10⁹⁶(97-digit number)

39289607011160111489…43314156323971271681

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

7.857 × 10⁹⁶(97-digit number)

78579214022320222979…86628312647942543359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.857 × 10⁹⁶(97-digit number)

78579214022320222979…86628312647942543361

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

1.571 × 10⁹⁷(98-digit number)

15715842804464044595…73256625295885086719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.571 × 10⁹⁷(98-digit number)

15715842804464044595…73256625295885086721

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 652771

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 cc7a685362d8d150aa273fda72a3ff0299ef23485adb33ee7a9ca7a16d59e571

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 #652,771 on Chainz ↗

Block #652,771

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