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Block #377,910

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 11:13:53 AM · Difficulty 10.4198 · 6,434,620 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

da1f2d53fa03f6a1530db8edb52b313210f98160b15f6efb2b3cc2973971b153

View on Chainz ↗

Height

#377,910

Difficulty

10.419805

Transactions

Size

660 B

Version

Bits

0a6b7858

Nonce

67,109,251

Timestamp

1/27/2014, 11:13:53 AM

Confirmations

6,434,620

Merkle Root

7f720a98356208a649b49362edb6defc14a413f2bfbf4c89092d783404c7e1cd

Transactions (3)

Coinbase5f18ecd3692fbe…7b412476e59df4

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

d27b65519d6786…46deb9aac37aa2

1 in → 2 out3.8302 XPM226 B

AXX9vGmK…CrKAX366 AJQmv4Xz…3YwRvmev

a0cafe905fa54f…246e14b880778e

1 in → 2 out2.1353 XPM226 B

AGLJWDwW…Nn8yuLu3 ARpzqnUm…DmQAk68w

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.

9.665 × 10⁹⁹(100-digit number)

96653324629176691352…74810626714830805760

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

9.665 × 10⁹⁹(100-digit number)

96653324629176691352…74810626714830805759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.665 × 10⁹⁹(100-digit number)

96653324629176691352…74810626714830805761

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

1.933 × 10¹⁰⁰(101-digit number)

19330664925835338270…49621253429661611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.933 × 10¹⁰⁰(101-digit number)

19330664925835338270…49621253429661611521

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

3.866 × 10¹⁰⁰(101-digit number)

38661329851670676540…99242506859323223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.866 × 10¹⁰⁰(101-digit number)

38661329851670676540…99242506859323223041

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

7.732 × 10¹⁰⁰(101-digit number)

77322659703341353081…98485013718646446079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.732 × 10¹⁰⁰(101-digit number)

77322659703341353081…98485013718646446081

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

1.546 × 10¹⁰¹(102-digit number)

15464531940668270616…96970027437292892159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.546 × 10¹⁰¹(102-digit number)

15464531940668270616…96970027437292892161

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 377910

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 da1f2d53fa03f6a1530db8edb52b313210f98160b15f6efb2b3cc2973971b153

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 #377,910 on Chainz ↗

Block #377,910

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