Home/Chain Registry/Block #860,363

Block #860,363

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/20/2014, 5:10:18 AM · Difficulty 10.9643 · 5,972,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a712aece457abd01229216ba6e4b74891042aedada0231b1d3de77661e1855ab

View on Chainz ↗

Height

#860,363

Difficulty

10.964325

Transactions

Size

27.74 KB

Version

Bits

0af6de09

Nonce

693,684,950

Timestamp

12/20/2014, 5:10:18 AM

Confirmations

5,972,211

Merkle Root

e100ed188d69ead07f97739ae81b27fe1aa5daf91b450b5192893204f72a1aa8

Transactions (4)

Coinbase8e67bfaa071edb…e6d8a4f3f729e2

1 in → 1 out8.6100 XPM116 B

ANSXnLY2…Sd25TjkD

3ca4a88c57a1a1…636cf512263f3a

2 in → 2 out10.7244 XPM375 B

ALEQQTfr…CcGmbuHa AW8DALNX…jkUjy6wv

f5d588a93f11ca…ee83ac784d8514

186 in → 2 out6.7840 XPM26.95 KB

AX3smubN…NiLNhvJW AYeGLxtJ…3XFCDFMm

ae36e01c317a61…d14662aa7fac8a

1 in → 2 out3.7000 XPM225 B

AHRoBSh4…BSVTQ36Q ASUg5CFq…6nXAwUVS

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.

4.338 × 10⁹⁴(95-digit number)

43389709136063311405…54975388082579053120

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

4.338 × 10⁹⁴(95-digit number)

43389709136063311405…54975388082579053119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.338 × 10⁹⁴(95-digit number)

43389709136063311405…54975388082579053121

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

8.677 × 10⁹⁴(95-digit number)

86779418272126622811…09950776165158106239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.677 × 10⁹⁴(95-digit number)

86779418272126622811…09950776165158106241

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

1.735 × 10⁹⁵(96-digit number)

17355883654425324562…19901552330316212479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.735 × 10⁹⁵(96-digit number)

17355883654425324562…19901552330316212481

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

3.471 × 10⁹⁵(96-digit number)

34711767308850649124…39803104660632424959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.471 × 10⁹⁵(96-digit number)

34711767308850649124…39803104660632424961

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

6.942 × 10⁹⁵(96-digit number)

69423534617701298249…79606209321264849919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.942 × 10⁹⁵(96-digit number)

69423534617701298249…79606209321264849921

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.388 × 10⁹⁶(97-digit number)

13884706923540259649…59212418642529699839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 860363

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 a712aece457abd01229216ba6e4b74891042aedada0231b1d3de77661e1855ab

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 #860,363 on Chainz ↗

Block #860,363

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