Home/Chain Registry/Block #277,714

Block #277,714

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 4:34:36 PM · Difficulty 9.9671 · 6,553,088 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91b4fc2886b6a73ff53d8328adfb4c3f48db63b06ebc950bd194ee2e57364f83

View on Chainz ↗

Height

#277,714

Difficulty

9.967059

Transactions

Size

1.69 KB

Version

Bits

09f79134

Nonce

27,005

Timestamp

11/27/2013, 4:34:36 PM

Confirmations

6,553,088

Merkle Root

e8d8fac9b558b267b8720ef8ce5044a172a28c97ad759b69dc29364640404be3

Transactions (2)

Coinbase00a5f445619ad9…c59ffb0fdd706e

1 in → 30 out10.0300 XPM1.06 KB

AcP9aGkN…9c7TeeiQ ANmkKL2U…jPxj1Qs3 ARy21REr…6pBWtQJ2 AWA5FEzr…x9RdPKTy Abv8pzf1…t4zPXDTV

fe08d5bcc861f7…960503cf33fc3a

3 in → 3 out228.8674 XPM557 B

AGBfRsNP…eLtQKj76 AdS1mNKo…yywpGnSy ARo32Xqg…2DSaRuZA

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.

2.650 × 10⁹⁵(96-digit number)

26508980411761886754…78741441703394837720

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

2.650 × 10⁹⁵(96-digit number)

26508980411761886754…78741441703394837719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.650 × 10⁹⁵(96-digit number)

26508980411761886754…78741441703394837721

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

5.301 × 10⁹⁵(96-digit number)

53017960823523773509…57482883406789675439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.301 × 10⁹⁵(96-digit number)

53017960823523773509…57482883406789675441

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

1.060 × 10⁹⁶(97-digit number)

10603592164704754701…14965766813579350879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.060 × 10⁹⁶(97-digit number)

10603592164704754701…14965766813579350881

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

2.120 × 10⁹⁶(97-digit number)

21207184329409509403…29931533627158701759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.120 × 10⁹⁶(97-digit number)

21207184329409509403…29931533627158701761

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

4.241 × 10⁹⁶(97-digit number)

42414368658819018807…59863067254317403519

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 277714

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 91b4fc2886b6a73ff53d8328adfb4c3f48db63b06ebc950bd194ee2e57364f83

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 #277,714 on Chainz ↗

Block #277,714

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