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Block #451,864

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 6:07:21 AM · Difficulty 10.3797 · 6,375,075 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a62d2f3835fb8dd67e3b5d929896fc71a4ca66d91624d772757d95f24a26337

View on Chainz ↗

Height

#451,864

Difficulty

10.379724

Transactions

Size

1.10 KB

Version

Bits

0a61359e

Nonce

295,350

Timestamp

3/20/2014, 6:07:21 AM

Confirmations

6,375,075

Merkle Root

6eba318c5be4d882493ab73c55f46d24e880b506b9c890f68f8384fbaf11a9d4

Transactions (2)

Coinbasefe9b76f21d5077…cf120939d6f339

1 in → 22 out9.2800 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AVSSoqRA…aFjFn3Zm AMW1p9oT…2TzdaZxH

6cca61c6eeb4ac…468b900d8c8808

1 in → 2 out8.2630 XPM227 B

ARxBFuHc…uBaS5oqe AYYCXV9U…EDLqydjJ

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.

1.080 × 10⁹³(94-digit number)

10800021615708193654…58249234471358069760

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

1.080 × 10⁹³(94-digit number)

10800021615708193654…58249234471358069759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.080 × 10⁹³(94-digit number)

10800021615708193654…58249234471358069761

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

2.160 × 10⁹³(94-digit number)

21600043231416387308…16498468942716139519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.160 × 10⁹³(94-digit number)

21600043231416387308…16498468942716139521

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

4.320 × 10⁹³(94-digit number)

43200086462832774616…32996937885432279039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.320 × 10⁹³(94-digit number)

43200086462832774616…32996937885432279041

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

8.640 × 10⁹³(94-digit number)

86400172925665549233…65993875770864558079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.640 × 10⁹³(94-digit number)

86400172925665549233…65993875770864558081

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

1.728 × 10⁹⁴(95-digit number)

17280034585133109846…31987751541729116159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.728 × 10⁹⁴(95-digit number)

17280034585133109846…31987751541729116161

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 451864

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 9a62d2f3835fb8dd67e3b5d929896fc71a4ca66d91624d772757d95f24a26337

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 #451,864 on Chainz ↗

Block #451,864

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