Home/Chain Registry/Block #277,870

Block #277,870

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 6:08:10 PM · Difficulty 9.9675 · 6,558,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f00525ac44c8d4a0a0b2832cb027c4b810571a7588217e3374649ff6fa2ac908

View on Chainz ↗

Height

#277,870

Difficulty

9.967472

Transactions

Size

2.37 KB

Version

Bits

09f7ac39

Nonce

13,192

Timestamp

11/27/2013, 6:08:10 PM

Confirmations

6,558,884

Merkle Root

e840177a74686a98e0ce73a27ceeaed25122fead2e77813f37630249dbf3c11c

Transactions (3)

Coinbase3132dcd1d6dbc7…afd73c8024256b

1 in → 2 out10.0986 XPM142 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

350a45cbe816e1…797e7e67d592f1

13 in → 1 out2.6900 XPM1.92 KB

ATA7GY8j…t8sAvuaw

1e62033f460d1e…ec74cbad1fc784

1 in → 2 out2.4782 XPM225 B

AGJmCkd8…vipYW3t9 ARyczVdC…dBz93pBz

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.

1.472 × 10¹⁰³(104-digit number)

14725757369414653898…18578136992662112660

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

1.472 × 10¹⁰³(104-digit number)

14725757369414653898…18578136992662112659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.472 × 10¹⁰³(104-digit number)

14725757369414653898…18578136992662112661

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

2.945 × 10¹⁰³(104-digit number)

29451514738829307796…37156273985324225319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.945 × 10¹⁰³(104-digit number)

29451514738829307796…37156273985324225321

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

5.890 × 10¹⁰³(104-digit number)

58903029477658615593…74312547970648450639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.890 × 10¹⁰³(104-digit number)

58903029477658615593…74312547970648450641

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

1.178 × 10¹⁰⁴(105-digit number)

11780605895531723118…48625095941296901279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.178 × 10¹⁰⁴(105-digit number)

11780605895531723118…48625095941296901281

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

2.356 × 10¹⁰⁴(105-digit number)

23561211791063446237…97250191882593802559

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 277870

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 f00525ac44c8d4a0a0b2832cb027c4b810571a7588217e3374649ff6fa2ac908

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 #277,870 on Chainz ↗

Block #277,870

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