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Block #150,747

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 6:00:47 AM · Difficulty 9.8589 · 6,674,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

465405ba342588a32505a0261e1bab3b73bb7a0f2803ac50134f85ffb7d434bb

View on Chainz ↗

Height

#150,747

Difficulty

9.858880

Transactions

Size

739 B

Version

Bits

09dbdf8a

Nonce

167,062

Timestamp

9/5/2013, 6:00:47 AM

Confirmations

6,674,564

Merkle Root

f2249bec64618fbbb3fd2c13ebb9c2a46d5c37c0041d186d1f640e0eeeb3e09b

Transactions (4)

Coinbase0d0edd41eaa446…587e2a41bdcb10

1 in → 1 out10.3000 XPM109 B

AMjazV56…tVUuP32T

e55599b849c518…13273a85de486e

1 in → 1 out10.2800 XPM158 B

AUQWNLX2…FxwsS5kV

a96e371b6e9645…f9778b47d48b29

1 in → 2 out10.2800 XPM192 B

AFz9fXym…wh4UqpkL AcF1GByq…fYwyK2nm

2c3a1357435ed7…4502d5906fd03c

1 in → 2 out10.2800 XPM192 B

AZFQK1Rg…MhdrYLXF AFz9fXym…wh4UqpkL

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.

1.535 × 10⁹⁰(91-digit number)

15357846509968079533…62513847308054237300

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

1.535 × 10⁹⁰(91-digit number)

15357846509968079533…62513847308054237299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.535 × 10⁹⁰(91-digit number)

15357846509968079533…62513847308054237301

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

3.071 × 10⁹⁰(91-digit number)

30715693019936159066…25027694616108474599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.071 × 10⁹⁰(91-digit number)

30715693019936159066…25027694616108474601

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

6.143 × 10⁹⁰(91-digit number)

61431386039872318133…50055389232216949199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.143 × 10⁹⁰(91-digit number)

61431386039872318133…50055389232216949201

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

1.228 × 10⁹¹(92-digit number)

12286277207974463626…00110778464433898399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.228 × 10⁹¹(92-digit number)

12286277207974463626…00110778464433898401

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

2.457 × 10⁹¹(92-digit number)

24572554415948927253…00221556928867796799

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 150747

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 465405ba342588a32505a0261e1bab3b73bb7a0f2803ac50134f85ffb7d434bb

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 #150,747 on Chainz ↗

Block #150,747

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