Block #267,204

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 2:13:25 AM · Difficulty 9.9594 · 6,529,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb6f6ea61b5aae5a049ff103e1fd0006476ee7170245a331e0e31062f906bf6b

View on Chainz ↗

Height

#267,204

Difficulty

9.959397

Transactions

Size

1.22 KB

Version

Bits

09f59b11

Nonce

17,502

Timestamp

11/21/2013, 2:13:25 AM

Confirmations

6,529,010

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

fbad64653a8acc80c699ab063e8dff3c02787e7453ab7cca0a48731327ced1f1

Transactions (5)

Coinbase961d2aea9ee9df…7a5bb910d9be26

1 in → 2 out10.1100 XPM141 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

d28966c567d446…529ec75ea884f7

2 in → 1 out206.8900 XPM341 B

AP5pfdXr…rf6fCGXP

401e756f401a4e…9d1cef1cb07a4f

1 in → 2 out10.0200 XPM225 B

ATkXJMZf…B1Uf2K4N AVJGTS9y…MTnSSkqs

6c18a8d21bfaca…e14ba2de1ff969

1 in → 2 out8.0065 XPM226 B

AcAxsY84…xUwUeFYT AcWit1Cz…NvsZFuz2

71cf39ce4c645f…f44bc016787a9b

1 in → 2 out2.9603 XPM227 B

AR4MQXSZ…QxvMLZ5w AaVFHFSq…bCnX1Bpw

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.

6.075 × 10¹⁰²(103-digit number)

60752023729674505785…54681889125594259839

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

6.075 × 10¹⁰²(103-digit number)

60752023729674505785…54681889125594259839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.075 × 10¹⁰²(103-digit number)

60752023729674505785…54681889125594259841

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

1.215 × 10¹⁰³(104-digit number)

12150404745934901157…09363778251188519679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.215 × 10¹⁰³(104-digit number)

12150404745934901157…09363778251188519681

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

2.430 × 10¹⁰³(104-digit number)

24300809491869802314…18727556502377039359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.430 × 10¹⁰³(104-digit number)

24300809491869802314…18727556502377039361

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

4.860 × 10¹⁰³(104-digit number)

48601618983739604628…37455113004754078719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.860 × 10¹⁰³(104-digit number)

48601618983739604628…37455113004754078721

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

9.720 × 10¹⁰³(104-digit number)

97203237967479209256…74910226009508157439

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Cross-reference on Chainz Explorer